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Liu, Chun

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Author ID: liu.chun Recent zbMATH articles by "Liu, Chun"
Published as: Liu, C.; Liu, Chun
Documents Indexed: 161 Publications since 1987, including 2 Books
all top 5

Co-Authors

1 single-authored
14 Shen, Jie
12 Du, Qiang
9 Calderer, Maria-Carme T.
9 Hyon, Yunkyong
8 Feng, James J.
8 Lin, Fang Hua
8 Yue, Xingye
7 Wang, Xiaoqiang
6 Ryham, Rolf J.
6 Xu, Shixin
6 Yue, Pengtao
5 Lin, Taichia
5 Yang, Xiaofeng
4 Duan, Chenghua
4 Walkington, Noel J.
4 Wu, Hao
3 Brannick, James J.
3 Chen, Minxin
3 Eisenberg, Bob
3 Giga, Yoshikazu
3 Jiang, Bin
3 Lai, Mingjun
3 Lee, Hijin
3 Lin, Ping
3 Liu, Lishan
3 Liu, Pei
3 Sheng, Ping
3 Tan, Zhong
3 Wang, Cheng
3 Wenston, Paul R.
3 Xu, Jinchao
3 Xu, Xiang
3 Zhang, Ke
2 Forest, M. Gregory
2 Hsieh, Chia-Yu
2 Huang, Tao
2 Koba, Hajime
2 Lee, Chiun-Chang
2 Lei, Zhen
2 Li, Shuwang
2 Li, Xiantao
2 Lu, Min-Jhe
2 Ma, Lina
2 Ma, Tianbao
2 Majd, Sheereen
2 Ning, Jianguo
2 Qian, Tiezheng
2 Sato, Norifumi
2 Schlömerkemper, Anja
2 Sun, Huan
2 Sun, Pengtao
2 Tonegawa, Yoshihiro
2 Voss, Karl
2 Wang, Qi
2 Wang, Yiwei
2 Wang, Yong
2 Wu, Yonghong
2 Yu, Peng
2 Zhang, Ping
2 Zhou, Yi
2 Zikatanov, Ludmil T.
1 Adler, James H.
1 Alvarez, Sergio A.
1 Ambrosi, Davide
1 Baek, Seungik
1 Bauman, Patricia E.
1 Belmonte, Andrew
1 Benešová, Barbora
1 Carrillo de la Plata, José Antonio
1 Chan, Christina K.
1 Chen, Falai
1 Chen, Geng
1 Chen, Gui-Qiang G.
1 Chen, Wenbin
1 Chen, Xinfu
1 Cheng, Qing
1 De Anna, Francesco
1 deForest, Russ
1 Deng, Chao
1 Ding, Xiao-yu
1 Du, Yi
1 Eisenberg, Robert S.
1 Endo, Masakazu
1 Fang, Daoyuan
1 Feng, Xiaobing
1 Fonseca, James E.
1 Forster, Johannes
1 García-Cervera, Carlos J.
1 Gharahi, Hamidreza
1 Golovaty, Dmitry
1 Götz, Dario
1 Gou, Kun
1 Guo, Limin
1 Hao, Wenrui
1 He, Yinnian
1 Hou, Thomas Yizhao
1 Hua, Jinsong
1 Jiang, Feng
1 Jiang, Jie
1 Jifara, Worku
...and 60 more Co-Authors
all top 5

Serials

13 Journal of Computational Physics
11 Communications in Mathematical Sciences
9 Archive for Rational Mechanics and Analysis
6 Discrete and Continuous Dynamical Systems
5 SIAM Journal on Mathematical Analysis
5 Discrete and Continuous Dynamical Systems. Series B
4 Journal of Differential Equations
4 Physica D
3 Communications on Pure and Applied Mathematics
3 SIAM Journal on Numerical Analysis
3 SIAM Journal on Applied Mathematics
3 Multiscale Modeling & Simulation
3 Communications in Computational Physics
2 Applicable Analysis
2 International Journal of Engineering Science
2 Journal of Fluid Mechanics
2 Mathematical Methods in the Applied Sciences
2 Nonlinearity
2 Quarterly of Applied Mathematics
2 Journal of Non-Newtonian Fluid Mechanics
2 SIAM Journal on Scientific Computing
2 Physics of Fluids
2 Interfaces and Free Boundaries
2 Oberwolfach Reports
2 Series in Contemporary Applied Mathematics CAM
2 Numerical Mathematics: Theory, Methods and Applications
2 Journal of Nonlinear Science and Applications
2 Computational and Mathematical Biophysics
1 Modern Physics Letters A
1 Computer Methods in Applied Mechanics and Engineering
1 Discrete Applied Mathematics
1 Journal of Mathematical Analysis and Applications
1 Mathematics of Computation
1 Bulletin of Mathematical Biology
1 BIT
1 Journal of Functional Analysis
1 Acta Scientiarum Naturalium Universitatis Sunyatseni
1 Circuits, Systems, and Signal Processing
1 Numerical Methods for Partial Differential Equations
1 Journal of Scientific Computing
1 Economics Letters
1 Differential and Integral Equations
1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1 Journal of Elasticity
1 Journal of Partial Differential Equations
1 Continuum Mechanics and Thermodynamics
1 Calculus of Variations and Partial Differential Equations
1 Journal of Mathematical Fluid Mechanics
1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
1 Journal of High Energy Physics
1 JP Journal of Algebra, Number Theory and Applications
1 Communications on Pure and Applied Analysis
1 Journal of Applied Mathematics and Computing
1 Transactions of Beijing Institute of Technology
1 Chinese Journal of Computational Mechanics
1 Journal of Hefei University of Technology. Natural Science
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Progress of Theoretical Physics. Supplement
1 Acta Mathematica Sinica. Chinese Series
1 Kinetic and Related Models
1 Journal of Computer Applications
1 Communications in Theoretical Physics
1 Molecular Based Mathematical Biology
1 International Journal of Systems Science. Principles and Applications of Systems and Integration
1 Annals of Mathematical Sciences and Applications
1 IEEE Transactions on Control of Network Systems

Publications by Year

Citations contained in zbMATH

117 Publications have been cited 2,801 times in 1,379 Documents Cited by Year
Nonparabolic dissipative systems modeling the flow of liquid crystals. Zbl 0842.35084
Lin, Fang-Hua; Liu, Chun
267
1995
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Zbl 1092.76069
Liu, Chun; Shen, Jie
181
2003
A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
175
2004
On hydrodynamics of viscoelastic fluids. Zbl 1076.76006
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
135
2005
Existence of solutions for the Ericksen-Leslie system. Zbl 0963.35158
Lin, Fang-Hua; Liu, Chun
120
2000
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Zbl 1116.74384
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
113
2004
Preconditioned multigrid methods for unsteady incompressible flows. Zbl 0908.76064
Liu, C.; Zheng, X.; Sung, C. H.
110
1998
Global solutions for incompressible viscoelastic fluids. Zbl 1138.76017
Lei, Zhen; Liu, Chun; Zhou, Yi
107
2008
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319
Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie
88
2006
An Eulerian description of fluids containing viscoelastic particles. Zbl 1009.76093
Liu, Chun; Walkington, Noel J.
82
2001
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. Zbl 1086.74024
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
76
2006
Partial regularity of the dynamic system modeling the flow of liquid crystals. Zbl 0948.35098
Lin, Fang-Hua; Liu, Chun
66
1996
On energetic variational approaches in modeling the nematic liquid crystal flows. Zbl 1156.76007
Sun, Huan; Liu, Chun
48
2009
A phase field formulation of the Willmore problem. Zbl 1125.35366
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
48
2005
Static and dynamic theories of liquid crystals. Zbl 1433.82014
Lin, Fanghua; Liu, Chun
48
2001
Approximation of liquid crystal flows. Zbl 1040.76036
Liu, Chun; Walkington, Noel J.
45
2000
Analysis of finite element approximations of a phase field model for two-phase fluids. Zbl 1111.76028
Feng, Xiaobing; He, Yinnian; Liu, Chun
39
2007
On the general Ericksen-Leslie system: Parodi’s relation, well-posedness and stability. Zbl 1320.76010
Wu, Hao; Xu, Xiang; Liu, Chun
38
2013
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Zbl 1172.74016
Du, Qiang; Li, Manlin; Liu, Chun
38
2007
Global existence for a 2D incompressible viscoelastic model with small strain. Zbl 1132.76008
Lei, Zhen; Liu, Chun; Zhou, Yi
37
2007
A mathematical model for the hard sphere repulsion in ionic solutions. Zbl 1406.76089
Hyon, Yunkyong; Eisenberg, Bob; Liu, Chun
34
2011
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
34
2009
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
31
2005
Energetic variational approach in complex fluids: maximum dissipation principle. Zbl 1423.76380
Hyon, Yunkyong; Kwak, Do Young; Liu, Chun
29
2010
An energy law preserving \(C^0\) finite element scheme for simulating the kinematic effects in liquid crystal dynamics. Zbl 1133.65077
Lin, Ping; Liu, Chun; Zhang, Hui
29
2007
On a micro-macro model for polymeric fluids near equilibrium. Zbl 1113.76017
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
29
2007
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064
Liu, Chun; Shen, Jie; Yang, Xiaofeng
27
2015
An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao
25
2005
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
25
2005
Simulations of singularity dynamics in liquid crystal flows: a \(C^0\) finite element approach. Zbl 1101.82039
Lin, Ping; Liu, Chun
24
2006
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
22
2005
Retrieving topological information for phase field models. Zbl 1114.74044
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
22
2005
Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation. Zbl 1078.92004
Du, Q.; Liu, C.; Ryham, R.; Wang, X.
21
2005
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112
Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai
20
2013
New Poisson-Boltzmann type equations: one-dimensional solutions. Zbl 1214.78012
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
20
2011
Mixed methods for the approximation of liquid crystal flows. Zbl 1032.76035
Liu, Chun; Walkington, Noel J.
20
2002
Evolution of grain boundaries. Zbl 1036.74041
Kinderlehrer, David; Liu, Chun
20
2001
Energy law preserving \(C^0\) finite element schemes for phase field models in two-phase flow computations. Zbl 1408.76550
Hua, Jinsong; Lin, Ping; Liu, Chun; Wang, Qi
19
2011
Finite time singularity of the nematic liquid crystal flow in dimension three. Zbl 1344.35104
Huang, Tao; Lin, Fanghua; Liu, Chun; Wang, Changyou
18
2016
Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions. Zbl 1412.34099
Liu, Lishan; Li, Hongdan; Liu, Chun; Wu, Yonghong
17
2017
Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343
Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil
17
2007
An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis. Zbl 1416.35209
Liu, Chun; Wu, Hao
16
2019
An energetic variational approach for ion transport. Zbl 1319.35199
Xu, Shixin; Sheng, Ping; Liu, Chun
16
2014
Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. Zbl 1138.76048
Liu, Chun; Walkington, Noel J.
16
2007
The phase transition between chiral nematic and smectic \(A^*\) liquid crystals. Zbl 1032.76007
Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel
16
2002
On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005
Liu, Chun; Shen, Jie
16
2001
Energetic variational approaches for incompressible fluid systems on an evolving surface. Zbl 1358.37081
Koba, Hajime; Liu, Chun; Giga, Yoshikazu
15
2017
Axisymmetric solutions to coupled Navier-Stokes/Allen-Cahn equations. Zbl 1203.35191
Xu, Xiang; Zhao, Liyun; Liu, Chun
15
2010
Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties. Zbl 1259.35040
Wu, Hao; Xu, Xiang; Liu, Chun
14
2012
Energy variational approach to study charge inversion (layering) near charged walls. Zbl 1257.82100
Hyon, Yunkyong; Fonseca, James E.; Eisenberg, Bob; Liu, Chun
14
2012
Shear cell rupture of nematic liquid crystal droplets in viscous fluids. Zbl 1282.76061
Yang, Xiaofeng; Forest, M. Gregory; Liu, Chun; Shen, Jie
14
2011
Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097
Sun, Pengtao; Liu, Chun; Xu, Jinchao
14
2009
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
14
2007
On electro-kinetic fluids: one-dimensional configurations. Zbl 1184.35262
Ryham, Rolf; Liu, Chun; Wang, Zhi-Qiang
12
2006
Dynamic theory for incompressible smectic-A liquid crystals: existence and regularity. Zbl 1021.35083
Liu, Chun
12
2000
Energetically stable discretizations for charge transport and electrokinetic models. Zbl 1351.78040
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
11
2016
Diffusion limit of kinetic equations for multiple species charged particles. Zbl 1308.35311
Wu, Hao; Lin, Tai-Chia; Liu, Chun
10
2015
A model of electrodiffusion and osmotic water flow and its energetic structure. Zbl 1227.92007
Mori, Yoichiro; Liu, Chun; Eisenberg, Robert S.
10
2011
Transient drop deformation upon startup of shear in viscoelastic fluids. Zbl 1188.76180
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
10
2005
From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids. Zbl 1108.76007
Yu, Peng; Du, Qiang; Liu, Chun
10
2005
Time evolution of nematic liquid crystals with variable degree of orientation. Zbl 1003.35108
Calderer, M. C.; Golovaty, D.; Lin, F.-H.; Liu, C.
9
2002
Transport of charged particles: entropy production and maximum dissipation principle. Zbl 1345.76123
Hsieh, Chia-Yu; Hyon, YunKyong; Lee, Hijin; Lin, Tai-Chia; Liu, Chun
8
2015
Existence and stability for mathematical models of sedimentation-consolidation processes in several space dimensions. Zbl 0995.35050
Bürger, R.; Liu, C.; Wendland, W. L.
8
2001
High order finite difference and multigrid methods for spatially evolving instability in a planar channel. Zbl 0769.76038
Liu, C.; Liu, Z.
8
1993
Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamic consistency. Zbl 1429.76032
De Anna, Francesco; Liu, Chun
7
2019
Modeling and simulating asymmetrical conductance changes in gramicidin pores. Zbl 1323.92090
Xu, Shixin; Chen, Minxin; Majd, Sheereen; Yue, Xingye; Liu, Chun
7
2014
Boundary layer solutions of charge conserving Poisson-Boltzmann equations: one-dimensional case. Zbl 1344.76077
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
6
2016
Two-phase flow problem coupled with mean curvature flow. Zbl 1246.35212
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
6
2012
Liquid crystal flow: Dynamic and static configurations. Zbl 0956.35104
Calderer, M. Carme; Liu, Chun
6
2000
Radial configurations of smectic A materials and focal conics. Zbl 0954.76004
Calderer, M. Carme; Liu, Chun; Voss, Karl
6
1998
Numerical simulations of hydrodynamics of nematic liquid crystals: effects of kinematic transports. Zbl 1364.76018
Zhang, Shupeng; Liu, Chun; Zhang, Hui
5
2011
On the existence of mean curvature flow with transport term. Zbl 1201.53076
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
5
2010
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
5
2008
Numerical complete solution for random genetic drift by energetic variational approach. Zbl 1418.65150
Duan, Chenghua; Liu, Chun; Wang, Cheng; Yue, Xingye
4
2019
A generalized Poisson-Nernst-Planck-Navier-Stokes model on the fluid with the crowded charged particles: derivation and its well-posedness. Zbl 1416.35220
Wang, Yong; Liu, Chun; Tan, Zhong
4
2016
Finite time singularities for hyperbolic systems. Zbl 1316.35005
Chen, Geng; Huang, Tao; Liu, Chun
4
2015
First-order system least squares and the energetic variational approach for two-phase flow. Zbl 1408.76528
Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L.
4
2011
An enhanced macroscopic closure approximation to the micro-macro FENE model for polymeric materials. Zbl 1173.76001
Hyon, Yunkyong; Du, Qiang; Liu, Chun
4
2008
Diffuse interface energies capturing the Euler number: relaxation and renomalization. Zbl 1136.74007
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
4
2007
Smectic A liquid crystal configurations with interface defects. Zbl 0988.76008
Calderer, M. Carme; Liu, Chun; Voss, Karl
4
2001
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
3
2020
Non-isothermal electrokinetics: energetic variational approach. Zbl 1406.35290
Liu, Pei; Wu, Simo; Liu, Chun
3
2018
Inventory competition in a dual-channel supply chain with delivery lead time consideration. Zbl 1443.90081
Yang, J. Q.; Zhang, X. M.; Fu, H. Y.; Liu, C.
3
2017
Existence of positive solutions for singular higher-order fractional differential equation via spectral analysis. Zbl 1377.34011
Guo, Limin; Liu, Chun
3
2017
Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid. Zbl 1369.35057
Endo, Masakazu; Giga, Yoshikazu; Götz, Dario; Liu, Chun
3
2017
Diffuse interface methods for multiple phase materials: an energetic variational approach. Zbl 1349.76759
Brannick, J.; Liu, C.; Qian, T.; Sun, H.
3
2015
An improved interpolating element-free Galerkin method based on nonsingular weight functions. Zbl 1407.74091
Sun, F. X.; Liu, C.; Cheng, Y. M.
3
2014
Heart-shaped bubbles rising in anisotropic liquids. Zbl 1146.76583
Zhou, Chunfeng; Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
3
2007
On two nonlinear biharmonic evolution equations: existence, uniqueness and stability. Zbl 1071.35042
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
3
2004
Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation. Zbl 1075.76040
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
3
2003
Existence of weak solutions to an evolutionary model for magnetoelasticity. Zbl 1390.74059
Benešová, Barbora; Forster, Johannes; Liu, Chun; Schlömerkemper, Anja
2
2018
Two-phase incompressible flows with variable density: an energetic variational approach. Zbl 1361.35129
Jiang, Jie; Li, Yinghua; Liu, Chun
2
2017
Strong solutions and instability for the fitness gradient system in evolutionary games between two populations. Zbl 1372.37137
Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong
2
2017
Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles. Zbl 1352.35127
Wang, Yong; Liu, Chun; Tan, Zhong
2
2017
Strong convergence of a general iterative algorithm for asymptotically nonexpansive semigroups in Banach spaces. Zbl 06807276
Liu, Lishan; Liu, Chun; Wang, Fang; Wu, Yonghong
2
2016
Blow-up criterion for compressible visco-elasticity equations in three dimensional space. Zbl 1301.35103
Du, Yi; Liu, Chun; Zhang, Qingtian
2
2014
Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Zbl 1282.76179
Liu, Chun; Qian, Tiezheng; Xu, Xinpeng
2
2012
Onsager principle and electrorheological fluid dynamics. Zbl 1167.82018
Sheng, Ping; Zhang, Jianwei; Liu, Chun
2
2008
Numerical simulations on two nonlinear biharmonic evolution equations. Zbl 1051.65098
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2
2004
Mathematical developments in the study of smectic A liquid crystals. Zbl 1210.76024
Calderer, M. Carme; Liu, Chun
2
2000
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
3
2020
On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach. Zbl 1437.76041
Liu, Chun; Wang, Yiwei
1
2020
An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis. Zbl 1416.35209
Liu, Chun; Wu, Hao
16
2019
Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamic consistency. Zbl 1429.76032
De Anna, Francesco; Liu, Chun
7
2019
Numerical complete solution for random genetic drift by energetic variational approach. Zbl 1418.65150
Duan, Chenghua; Liu, Chun; Wang, Cheng; Yue, Xingye
4
2019
Numerical methods for porous medium equation by an energetic variational approach. Zbl 1451.76118
Duan, Chenghua; Liu, Chun; Wang, Cheng; Yue, Xingye
1
2019
Nonlinear simulation of an elastic tumor-host interface. Zbl 1425.92115
Lu, Min-Jhe; Liu, Chun; Li, Shuwang
1
2019
Hierarchical-structure-based fault estimation and fault-tolerant control for multiagent systems. Zbl 07093922
Liu, Chun; Jiang, Bin; Patton, Ron J.; Zhang, Ke
1
2019
Non-isothermal electrokinetics: energetic variational approach. Zbl 1406.35290
Liu, Pei; Wu, Simo; Liu, Chun
3
2018
Existence of weak solutions to an evolutionary model for magnetoelasticity. Zbl 1390.74059
Benešová, Barbora; Forster, Johannes; Liu, Chun; Schlömerkemper, Anja
2
2018
Integrated multiple-model adaptive fault identification and reconfigurable fault-tolerant control for lead-wing close formation systems. Zbl 1385.93041
Liu, Chun; Jiang, Bin; Zhang, Ke
1
2018
Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions. Zbl 1412.34099
Liu, Lishan; Li, Hongdan; Liu, Chun; Wu, Yonghong
17
2017
Energetic variational approaches for incompressible fluid systems on an evolving surface. Zbl 1358.37081
Koba, Hajime; Liu, Chun; Giga, Yoshikazu
15
2017
Inventory competition in a dual-channel supply chain with delivery lead time consideration. Zbl 1443.90081
Yang, J. Q.; Zhang, X. M.; Fu, H. Y.; Liu, C.
3
2017
Existence of positive solutions for singular higher-order fractional differential equation via spectral analysis. Zbl 1377.34011
Guo, Limin; Liu, Chun
3
2017
Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid. Zbl 1369.35057
Endo, Masakazu; Giga, Yoshikazu; Götz, Dario; Liu, Chun
3
2017
Two-phase incompressible flows with variable density: an energetic variational approach. Zbl 1361.35129
Jiang, Jie; Li, Yinghua; Liu, Chun
2
2017
Strong solutions and instability for the fitness gradient system in evolutionary games between two populations. Zbl 1372.37137
Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong
2
2017
Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles. Zbl 1352.35127
Wang, Yong; Liu, Chun; Tan, Zhong
2
2017
Largest well-posed spaces for the general diffusion system with nonlocal interactions. Zbl 1372.35309
Deng, Chao; Liu, Chun
1
2017
On partial regularity problem for 3D Boussinesq equations. Zbl 1372.35233
Fang, Daoyuan; Liu, Chun; Qian, Chenyin
1
2017
Finite time singularity of the nematic liquid crystal flow in dimension three. Zbl 1344.35104
Huang, Tao; Lin, Fanghua; Liu, Chun; Wang, Changyou
18
2016
Energetically stable discretizations for charge transport and electrokinetic models. Zbl 1351.78040
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
11
2016
Boundary layer solutions of charge conserving Poisson-Boltzmann equations: one-dimensional case. Zbl 1344.76077
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
6
2016
A generalized Poisson-Nernst-Planck-Navier-Stokes model on the fluid with the crowded charged particles: derivation and its well-posedness. Zbl 1416.35220
Wang, Yong; Liu, Chun; Tan, Zhong
4
2016
Strong convergence of a general iterative algorithm for asymptotically nonexpansive semigroups in Banach spaces. Zbl 06807276
Liu, Lishan; Liu, Chun; Wang, Fang; Wu, Yonghong
2
2016
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064
Liu, Chun; Shen, Jie; Yang, Xiaofeng
27
2015
Diffusion limit of kinetic equations for multiple species charged particles. Zbl 1308.35311
Wu, Hao; Lin, Tai-Chia; Liu, Chun
10
2015
Transport of charged particles: entropy production and maximum dissipation principle. Zbl 1345.76123
Hsieh, Chia-Yu; Hyon, YunKyong; Lee, Hijin; Lin, Tai-Chia; Liu, Chun
8
2015
Finite time singularities for hyperbolic systems. Zbl 1316.35005
Chen, Geng; Huang, Tao; Liu, Chun
4
2015
Diffuse interface methods for multiple phase materials: an energetic variational approach. Zbl 1349.76759
Brannick, J.; Liu, C.; Qian, T.; Sun, H.
3
2015
An energetic variational approach for ion transport. Zbl 1319.35199
Xu, Shixin; Sheng, Ping; Liu, Chun
16
2014
Modeling and simulating asymmetrical conductance changes in gramicidin pores. Zbl 1323.92090
Xu, Shixin; Chen, Minxin; Majd, Sheereen; Yue, Xingye; Liu, Chun
7
2014
An improved interpolating element-free Galerkin method based on nonsingular weight functions. Zbl 1407.74091
Sun, F. X.; Liu, C.; Cheng, Y. M.
3
2014
Blow-up criterion for compressible visco-elasticity equations in three dimensional space. Zbl 1301.35103
Du, Yi; Liu, Chun; Zhang, Qingtian
2
2014
An energetic variational approach to ion channel dynamics. Zbl 1302.35375
Hyon, YunKyong; Eisenberg, Bob; Liu, Chun
1
2014
On the general Ericksen-Leslie system: Parodi’s relation, well-posedness and stability. Zbl 1320.76010
Wu, Hao; Xu, Xiang; Liu, Chun
38
2013
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112
Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai
20
2013
High-order mixed weighted compact and non-compact scheme for shock and small length scale interaction. Zbl 1278.76049
Stipcich, G.; Fu, H.; Liu, C.
1
2013
\(\theta_{13}\) and the Higgs mass from high scale supersymmetry. Zbl 1264.81319
Liu, Chun; Zhao, Zhen-Hua
1
2013
Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties. Zbl 1259.35040
Wu, Hao; Xu, Xiang; Liu, Chun
14
2012
Energy variational approach to study charge inversion (layering) near charged walls. Zbl 1257.82100
Hyon, Yunkyong; Fonseca, James E.; Eisenberg, Bob; Liu, Chun
14
2012
Two-phase flow problem coupled with mean curvature flow. Zbl 1246.35212
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
6
2012
Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Zbl 1282.76179
Liu, Chun; Qian, Tiezheng; Xu, Xinpeng
2
2012
A mathematical model for the hard sphere repulsion in ionic solutions. Zbl 1406.76089
Hyon, Yunkyong; Eisenberg, Bob; Liu, Chun
34
2011
New Poisson-Boltzmann type equations: one-dimensional solutions. Zbl 1214.78012
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
20
2011
Energy law preserving \(C^0\) finite element schemes for phase field models in two-phase flow computations. Zbl 1408.76550
Hua, Jinsong; Lin, Ping; Liu, Chun; Wang, Qi
19
2011
Shear cell rupture of nematic liquid crystal droplets in viscous fluids. Zbl 1282.76061
Yang, Xiaofeng; Forest, M. Gregory; Liu, Chun; Shen, Jie
14
2011
A model of electrodiffusion and osmotic water flow and its energetic structure. Zbl 1227.92007
Mori, Yoichiro; Liu, Chun; Eisenberg, Robert S.
10
2011
Numerical simulations of hydrodynamics of nematic liquid crystals: effects of kinematic transports. Zbl 1364.76018
Zhang, Shupeng; Liu, Chun; Zhang, Hui
5
2011
First-order system least squares and the energetic variational approach for two-phase flow. Zbl 1408.76528
Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L.
4
2011
Energetic variational approach in complex fluids: maximum dissipation principle. Zbl 1423.76380
Hyon, Yunkyong; Kwak, Do Young; Liu, Chun
29
2010
Axisymmetric solutions to coupled Navier-Stokes/Allen-Cahn equations. Zbl 1203.35191
Xu, Xiang; Zhao, Liyun; Liu, Chun
15
2010
On the existence of mean curvature flow with transport term. Zbl 1201.53076
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
5
2010
On energetic variational approaches in modeling the nematic liquid crystal flows. Zbl 1156.76007
Sun, Huan; Liu, Chun
48
2009
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
34
2009
Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097
Sun, Pengtao; Liu, Chun; Xu, Jinchao
14
2009
Global solutions for incompressible viscoelastic fluids. Zbl 1138.76017
Lei, Zhen; Liu, Chun; Zhou, Yi
107
2008
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
5
2008
An enhanced macroscopic closure approximation to the micro-macro FENE model for polymeric materials. Zbl 1173.76001
Hyon, Yunkyong; Du, Qiang; Liu, Chun
4
2008
Onsager principle and electrorheological fluid dynamics. Zbl 1167.82018
Sheng, Ping; Zhang, Jianwei; Liu, Chun
2
2008
The nucleation and growth of gas bubbles in a Newtonian fluid: an energetic variational phase field approach. Zbl 1306.76050
Naber, Aaron; Liu, Chun; Feng, James J.
1
2008
Analysis of finite element approximations of a phase field model for two-phase fluids. Zbl 1111.76028
Feng, Xiaobing; He, Yinnian; Liu, Chun
39
2007
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Zbl 1172.74016
Du, Qiang; Li, Manlin; Liu, Chun
38
2007
Global existence for a 2D incompressible viscoelastic model with small strain. Zbl 1132.76008
Lei, Zhen; Liu, Chun; Zhou, Yi
37
2007
An energy law preserving \(C^0\) finite element scheme for simulating the kinematic effects in liquid crystal dynamics. Zbl 1133.65077
Lin, Ping; Liu, Chun; Zhang, Hui
29
2007
On a micro-macro model for polymeric fluids near equilibrium. Zbl 1113.76017
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
29
2007
Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343
Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil
17
2007
Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. Zbl 1138.76048
Liu, Chun; Walkington, Noel J.
16
2007
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
14
2007
Diffuse interface energies capturing the Euler number: relaxation and renomalization. Zbl 1136.74007
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
4
2007
Heart-shaped bubbles rising in anisotropic liquids. Zbl 1146.76583
Zhou, Chunfeng; Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
3
2007
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319
Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie
88
2006
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. Zbl 1086.74024
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
76
2006
Simulations of singularity dynamics in liquid crystal flows: a \(C^0\) finite element approach. Zbl 1101.82039
Lin, Ping; Liu, Chun
24
2006
On electro-kinetic fluids: one-dimensional configurations. Zbl 1184.35262
Ryham, Rolf; Liu, Chun; Wang, Zhi-Qiang
12
2006
A model for total energy of nematic elastomers with non-uniform prolate spheroids. Zbl 1118.82015
Calderer, Maria-Carme; Liu, Chun; Yan, Baisheng
1
2006
On hydrodynamics of viscoelastic fluids. Zbl 1076.76006
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
135
2005
A phase field formulation of the Willmore problem. Zbl 1125.35366
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
48
2005
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
31
2005
An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao
25
2005
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
25
2005
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
22
2005
Retrieving topological information for phase field models. Zbl 1114.74044
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
22
2005
Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation. Zbl 1078.92004
Du, Q.; Liu, C.; Ryham, R.; Wang, X.
21
2005
Transient drop deformation upon startup of shear in viscoelastic fluids. Zbl 1188.76180
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
10
2005
From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids. Zbl 1108.76007
Yu, Peng; Du, Qiang; Liu, Chun
10
2005
Dynamic steady-state stress field in a web during slitting. Zbl 1111.74522
Liu, C.; Lu, Hongbin; Huang, Young
1
2005
A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
175
2004
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Zbl 1116.74384
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
113
2004
On two nonlinear biharmonic evolution equations: existence, uniqueness and stability. Zbl 1071.35042
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
3
2004
Numerical simulations on two nonlinear biharmonic evolution equations. Zbl 1051.65098
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2
2004
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Zbl 1092.76069
Liu, Chun; Shen, Jie
181
2003
Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation. Zbl 1075.76040
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
3
2003
Mixed methods for the approximation of liquid crystal flows. Zbl 1032.76035
Liu, Chun; Walkington, Noel J.
20
2002
The phase transition between chiral nematic and smectic \(A^*\) liquid crystals. Zbl 1032.76007
Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel
16
2002
Time evolution of nematic liquid crystals with variable degree of orientation. Zbl 1003.35108
Calderer, M. C.; Golovaty, D.; Lin, F.-H.; Liu, C.
9
2002
Hierarchical shape modeling for automatic face localization. Zbl 1039.68675
Liu, C.; Shum, H.-Y.; Zhang, C.
1
2002
Axisymmetric configurations of bipolar liquid crystal droplets. Zbl 1023.76006
Shen, Quan; Liu, Chun; Calderer, M. Carme
1
2002
An Eulerian description of fluids containing viscoelastic particles. Zbl 1009.76093
Liu, Chun; Walkington, Noel J.
82
2001
...and 17 more Documents
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Cited by 1,927 Authors

49 Liu, Chun
39 Yang, Xiaofeng
31 Liu, Qiao
27 Shen, Jie
21 Wang, Qi
20 Guillén González, Francisco M.
17 Zhao, Jia
16 Fan, Jishan
16 Lowengrub, John Samuel
15 Hu, Xianpeng
15 Kim, Junseok
15 Wang, Changyou
15 Wang, Dehua
15 Zhao, Jihong
14 Yao, Zhengan
13 Du, Qiang
13 Wu, Hao
13 Zhang, Zhifei
12 Lin, Fang Hua
12 Rocca, Elisabetta
12 Zarnescu, Arghir Dani
11 Feng, James J.
11 Jiang, Fei
11 Lin, Ping
11 Wang, Xiaoqiang
11 Yue, Pengtao
10 Lei, Zhen
10 Nochetto, Ricardo Horacio
10 Schimperna, Giulio
10 Shu, Chang
10 Tan, Zhong
10 Voigt, Axel
10 Xu, Xiang
9 Ding, Shijin
9 Grasselli, Maurizio
9 Liu, Weishi
9 Wang, Wei
9 Xu, Jinchao
9 Zi, Ruizhao
8 Abels, Helmut
8 Barrett, John W.
8 Gal, Ciprian Gheorghe Sorin
8 Guo, Boling
8 Han, Daozhi
8 He, Xiaoming
8 Hieber, Matthias
8 Huang, Jinrui
8 Lee, Hyun Geun
8 Liu, Lishan
8 Mori, Yoichiro
8 Walker, Shawn W.
8 Wang, Cheng
8 Wise, Steven M.
8 Yuan, Baoquan
8 Zhang, Mingji
8 Zhang, Pingwen
7 Ding, Hang
7 Gong, Yuezheng
7 Huang, Tao
7 Li, Jinkai
7 Liu, Shengquan
7 Masmoudi, Nader
7 Miranville, Alain M.
7 Pan, Kejia
7 Sarkar, Kausik
7 Süli, Endre E.
7 Tachim Medjo, Theodore
7 Tonegawa, Yoshihiro
7 Wen, Huanyao
7 Yu, Haijun
7 Zhang, Ping
7 Zhang, Ting
7 Zhou, Yong
6 Adler, James H.
6 Afkhami, Shahriar
6 Calderer, Maria-Carme T.
6 Chen, Chuanjun
6 Climent-Ezquerra, Blanca
6 Dong, Suchuan
6 Fang, Daoyuan
6 Garcke, Harald
6 Ju, Lili
6 Lee, Chiun-Chang
6 Li, Shuwang
6 Li, Xiaoli
6 Li, Yin
6 Lin, Junyu
6 Liu, Xiangao
6 Ratiu, Tudor Stefan
6 Soldati, Alfredo
6 Sun, Shuyu
6 Tierra, Giordano
6 Wei, Ruiying
6 Wu, Yonghong
5 Anderson, Patrick D.
5 Bie, Qunyi
5 Chechkin, Gregory A.
5 Chen, Lizhen
5 Constantin, Peter
5 De Anna, Francesco
...and 1,827 more Authors
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Cited in 188 Serials

196 Journal of Computational Physics
67 Journal of Differential Equations
55 Archive for Rational Mechanics and Analysis
43 Computers and Fluids
43 Journal of Scientific Computing
38 Computer Methods in Applied Mechanics and Engineering
38 Journal of Mathematical Analysis and Applications
37 Journal of Fluid Mechanics
30 Computers & Mathematics with Applications
30 Mathematical Methods in the Applied Sciences
29 SIAM Journal on Mathematical Analysis
27 SIAM Journal on Scientific Computing
24 Journal of Computational and Applied Mathematics
24 Discrete and Continuous Dynamical Systems
22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
22 Journal of Mathematical Fluid Mechanics
21 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
17 ZAMP. Zeitschrift für angewandte Mathematik und Physik
17 SIAM Journal on Applied Mathematics
17 Communications on Pure and Applied Analysis
16 Physica D
16 Calculus of Variations and Partial Differential Equations
14 Applied Mathematics and Computation
14 Nonlinear Analysis. Real World Applications
13 Mathematics of Computation
13 Journal of Functional Analysis
12 Applied Numerical Mathematics
11 International Journal for Numerical Methods in Fluids
11 Journal of Mathematical Physics
11 Numerische Mathematik
11 Applied Mathematics Letters
11 Discrete and Continuous Dynamical Systems. Series B
11 Journal of Theoretical Biology
10 Communications in Mathematical Physics
9 Applicable Analysis
9 Communications on Pure and Applied Mathematics
9 SIAM Journal on Numerical Analysis
9 Acta Applicandae Mathematicae
9 Journal of Non-Newtonian Fluid Mechanics
9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Chinese Annals of Mathematics. Series B
8 Applied Mathematical Modelling
8 Physics of Fluids
7 Bulletin of Mathematical Biology
7 International Journal for Numerical Methods in Engineering
7 Boundary Value Problems
7 Discrete and Continuous Dynamical Systems. Series S
6 Mathematische Annalen
6 Quarterly of Applied Mathematics
6 Communications in Partial Differential Equations
6 European Journal of Mechanics. B. Fluids
6 Molecular Based Mathematical Biology
6 Journal of Function Spaces
5 Journal of Mathematical Biology
5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
5 Journal of Dynamics and Differential Equations
5 Journal of Nonlinear Science
5 Abstract and Applied Analysis
5 Journal of Evolution Equations
5 Science China. Mathematics
4 Journal of Statistical Physics
4 Nonlinearity
4 Advances in Mathematics
4 Mathematics and Computers in Simulation
4 European Journal of Applied Mathematics
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 NoDEA. Nonlinear Differential Equations and Applications
4 Advances in Computational Mathematics
4 Engineering Analysis with Boundary Elements
4 Communications in Nonlinear Science and Numerical Simulation
4 International Journal of Computational Methods
4 Computational and Mathematical Biophysics
3 Computer Physics Communications
3 International Journal of Engineering Science
3 Physica A
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Mathematische Nachrichten
3 Transactions of the American Mathematical Society
3 Computational Mechanics
3 Mathematical Problems in Engineering
3 Mathematical Physics, Analysis and Geometry
3 Acta Mathematica Sinica. English Series
3 Nonlinear Analysis. Modelling and Control
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Analysis and Applications (Singapore)
3 Frontiers of Mathematics in China
3 Kinetic and Related Models
2 Acta Mechanica
2 Mathematical Biosciences
2 Annales Polonici Mathematici
2 Calcolo
2 Meccanica
2 Numerical Methods for Partial Differential Equations
2 Mathematical and Computer Modelling
2 Numerical Algorithms
2 Journal of Mathematical Imaging and Vision
2 Potential Analysis
2 Applicationes Mathematicae
2 Computational and Applied Mathematics
2 International Journal of Numerical Methods for Heat & Fluid Flow
...and 88 more Serials
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Cited in 39 Fields

959 Fluid mechanics (76-XX)
749 Partial differential equations (35-XX)
405 Numerical analysis (65-XX)
163 Statistical mechanics, structure of matter (82-XX)
138 Mechanics of deformable solids (74-XX)
112 Biology and other natural sciences (92-XX)
46 Calculus of variations and optimal control; optimization (49-XX)
38 Classical thermodynamics, heat transfer (80-XX)
34 Differential geometry (53-XX)
33 Ordinary differential equations (34-XX)
24 Dynamical systems and ergodic theory (37-XX)
24 Optics, electromagnetic theory (78-XX)
19 Probability theory and stochastic processes (60-XX)
15 Operator theory (47-XX)
13 Global analysis, analysis on manifolds (58-XX)
9 Real functions (26-XX)
8 Harmonic analysis on Euclidean spaces (42-XX)
7 Operations research, mathematical programming (90-XX)
6 Integral equations (45-XX)
6 Geophysics (86-XX)
6 Systems theory; control (93-XX)
5 Computer science (68-XX)
4 Information and communication theory, circuits (94-XX)
3 Combinatorics (05-XX)
3 Functions of a complex variable (30-XX)
3 Functional analysis (46-XX)
3 Mechanics of particles and systems (70-XX)
3 Quantum theory (81-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Measure and integration (28-XX)
2 Approximations and expansions (41-XX)
2 Statistics (62-XX)
2 Astronomy and astrophysics (85-XX)
1 General and overarching topics; collections (00-XX)
1 Algebraic geometry (14-XX)
1 Special functions (33-XX)
1 Integral transforms, operational calculus (44-XX)
1 Algebraic topology (55-XX)
1 Relativity and gravitational theory (83-XX)

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