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## Robinson, James Cooper

Compute Distance To:
 Author ID: robinson.james-c Published as: Robinson, James C.; Robinson, J. C. Homepage: https://warwick.ac.uk/fac/sci/maths/people/staff/james_robinson/ External Links: MGP · ORCID · dblp
 Documents Indexed: 140 Publications since 1993, including 11 Books
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#### Co-Authors

 34 single-authored 26 Langa, Jose’ Antonio 13 Rodrigo, José Luis 13 Sadowski, Witold 9 Nolasco de Carvalho, Alexandre 9 Suárez, Antonio 9 Vidal-López, Alejandro 8 Olson, Eric J. 7 Caraballo Garrido, Tomás 6 McCormick, David S. 6 Sierżȩga, Mikołaj 5 Dashti, Masoumeh 5 Friz, Peter Karl 5 Rodríguez-Bernal, Aníbal 4 Laister, Robert 4 Marín-Rubio, Pedro 4 Pinto de Moura, Eleonora 3 Fefferman, Charles Louis 3 Sharples, Nicholas 2 Fraser, Jonathan MacDonald 2 Glendinning, Paul Alexander 2 Hajduk, Karol W. 2 Hoang, Luan Thach 2 Kukavica, Igor 2 Łukaszewicz, Grzegorz 2 Margaris, Alexandros 2 Pooley, Benjamin C. 2 Real Anguas, José 2 Sánchez-Gabites, Jaime J. 2 Skipper, Jack W. D. 1 Blömker, Dirk 1 Bosia, Stefano 1 Chemin, Jean-Yves 1 Chernyshenko, Sergei I. 1 Chipot, Michel 1 Constantin, Peter 1 Cotter, Simon L. 1 Crauel, Hans 1 Da Silva, Ricardo Parreira 1 Droniou, Jérôme 1 García-Luengo, Julia 1 Henderson, A. M. 1 Nieuwenhuis, Michaela A. C. 1 Nolde, Christian 1 Ożański, Wojciech Sławomir 1 Pata, Vittorino 1 Planas, Gabriela 1 Steinerberger, Stefan 1 Stuart, Andrew M. 1 Tearne, Oliver M. 1 Titi, Edriss Saleh 1 Xue, Wei 1 Zhou, Yi
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#### Serials

 16 Journal of Differential Equations 14 Nonlinearity 8 Journal of Mathematical Analysis and Applications 7 Discrete and Continuous Dynamical Systems 5 Proceedings of the American Mathematical Society 4 Physica D 4 Journal of Dynamics and Differential Equations 4 London Mathematical Society Lecture Note Series 3 Archive for Rational Mechanics and Analysis 3 Physics Letters. A 3 Advances in Mathematics 3 Real Analysis Exchange 3 SIAM Journal on Mathematical Analysis 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Discrete and Continuous Dynamical Systems. Series B 3 Stochastics and Dynamics 2 Communications in Mathematical Physics 2 Journal of Mathematical Physics 2 Asymptotic Analysis 2 Dynamic Systems and Applications 2 Journal of Mathematical Fluid Mechanics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Inverse Problems 1 Journal of Fluid Mechanics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Bulletin of the London Mathematical Society 1 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matematico della Università di Padova 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Systems & Control Letters 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Numerical Algorithms 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Set-Valued Analysis 1 Chaos 1 Revista Matemática Complutense 1 Communications on Pure and Applied Analysis 1 Milan Journal of Mathematics 1 Analysis and Applications (Singapore) 1 Dynamics of Partial Differential Equations 1 Applied Mathematical Sciences 1 Cambridge Studies in Advanced Mathematics 1 Cambridge Tracts in Mathematics 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 ISRN Mathematical Analysis 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Cambridge Texts in Applied Mathematics
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#### Fields

 88 Partial differential equations (35-XX) 58 Dynamical systems and ergodic theory (37-XX) 46 Fluid mechanics (76-XX) 31 Ordinary differential equations (34-XX) 12 General topology (54-XX) 10 Functional analysis (46-XX) 10 Probability theory and stochastic processes (60-XX) 8 Measure and integration (28-XX) 7 Operator theory (47-XX) 7 Numerical analysis (65-XX) 6 General and overarching topics; collections (00-XX) 5 Manifolds and cell complexes (57-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

119 Publications have been cited 2,077 times in 1,373 Documents Cited by Year
Infinite-dimensional dynamical systems. An introduction to dissipative parabolic PDEs and the theory of global attractors. Zbl 0980.35001
Robinson, James C.
2001
Introduction (to “From finite to infinite dimensional dynamical systems”). Zbl 1026.37500
Robinson, J. C.; Glendinning, P. A.
2001
Attractors for infinite-dimensional non-autonomous dynamical systems. Zbl 1263.37002
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2013
Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Zbl 1296.35142
Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2014
Upper semicontinuity of attractors for small random perturbations of dynamical systems. Zbl 0917.35169
Caraballo, Tomás; Langa, José A.; Robinson, James C.
1998
A comparison between two theories for multi-valued semiflows and their asymptotic behaviour. Zbl 1053.47050
Caraballo, T.; Marín-Rubio, P.; Robinson, J. C.
2003
Stability and random attractors for a reaction-diffusion equation with multiplicative noise. Zbl 1011.37031
Caraballo, Tomás; Langa, José A.; Robinson, James C.
2000
A stochastic pitchfork bifurcation in a reaction-diffusion equation. Zbl 0996.60070
Caraballo, Tomás; Langa, José A.; Robinson, James C.
2001
Dimensions, embeddings, and attractors. Zbl 1222.37004
Robinson, James C.
2011
The three-dimensional Navier-Stokes equations. Classical theory. Zbl 1358.35002
Robinson, James C.; Rodrigo, José L.; Sadowski, Witold
2016
Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Zbl 1119.37023
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.; Suárez, Antonio
2007
Stability, instability, and bifurcation phenomena in non-autonomous differential equations. Zbl 1004.37032
Langa, José A.; Robinson, James C.; Suárez, Antonio
2002
Local existence for the non-resistive MHD equations in Besov spaces. Zbl 1333.35183
Chemin, Jean-Yves; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2016
Stability of random attractors under perturbation and approximation. Zbl 1020.37033
Robinson, James C.
2002
Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation. Zbl 1282.35042
Carvalho, A. N.; Langa, J. A.; Robinson, J. C.
2012
Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces. Zbl 1359.35150
Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2017
Attractors for differential equations with variable delays. Zbl 0997.34073
Caraballo, Tomás; Langa, José A.; Robinson, James C.
2001
Bayesian inverse problems for functions and applications to fluid mechanics. Zbl 1228.35269
Cotter, S. L.; Dashti, M.; Robinson, J. C.; Stuart, A. M.
2009
A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. Zbl 1144.81329
Chernyshenko, Sergei I.; Constantin, Peter; Robinson, James C.; Titi, Edriss S.
2007
The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C.
2007
Fractal dimension of a random invariant set. Zbl 1134.37364
Langa, José A.; Robinson, James C.
2006
Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO. Zbl 1291.46029
McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2013
Global attractors: Topology and finite-dimensional dynamics. Zbl 0953.34049
Robinson, James C.
1999
Invariant measures for dissipative systems and generalised Banach limits. Zbl 1230.37094
Łukaszewicz, Grzegorz; Real, José; Robinson, James C.
2011
On the Assouad dimension of self-similar sets with overlaps. Zbl 1317.28014
Fraser, J. M.; Henderson, A. M.; Olson, E. J.; Robinson, J. C.
2015
Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces. Zbl 1425.76055
Robinson, James C.; Sadowski, Witold; Silva, Ricardo P.
2012
Invariant measures for non-autonomous dissipative dynamical systems. Zbl 1351.37076
Łukaszewicz, Grzegorz; Robinson, James C.
2014
Supersolutions for a class of semilinear heat equations. Zbl 1334.35169
Robinson, James C.; Sierżęga, Mikołaj
2013
On the continuity of pullback attractors for evolution processes. Zbl 1175.37078
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2009
Bifurcations in non-autonomous scalar equations. Zbl 1096.34026
Langa, J. A.; Robinson, J. C.; Suárez, A.
2006
Non-autonomous dynamical systems. Zbl 1384.37024
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2015
The stability of attractors for non-autonomous perturbations of gradient-like systems. Zbl 1115.37064
Langa, José A.; Robinson, James C.; Suárez, Antonio; Vidal-López, Alejandro
2007
A topological delay embedding theorem for infinite-dimensional dynamical systems. Zbl 1084.37063
Robinson, James C.
2005
Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1173.35631
2009
Lower semicontinuity of attractors for non-autonomous dynamical systems. Zbl 1181.37016
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2009
Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems. Zbl 1137.35009
Robinson, James C.; Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro
2007
Stabilisation of linear PDEs by Stratonovich noise. Zbl 1157.60332
Caraballo, Tomás; Robinson, James C.
2004
A weak-$$L^p$$ Prodi-Serrin type regularity criterion for the Navier-Stokes equations. Zbl 1307.35186
Bosia, Stefano; Pata, Vittorino; Robinson, James C.
2014
The asymptotic completeness of inertial manifolds. Zbl 0898.35016
Robinson, James C.
1996
Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations. Zbl 1120.35075
2007
On the dimension of the singular set of solutions to the Navier-Stokes equations. Zbl 1233.35162
2012
Almost bi-Lipschitz embeddings and almost homogeneous sets. Zbl 1197.54045
Olson, Eric J.; Robinson, James C.
2010
A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Zbl 1349.35169
Laister, R.; Robinson, J. C.; Sierżȩga, M.; Vidal-López, A.
2016
Attractors for the stochastic 3D Navier-Stokes equations. Zbl 1059.35100
Marín-Rubio, Pedro; Robinson, James C.
2003
Attractors and finite-dimensional behaviour in the 2D Navier-Stokes equations. Zbl 1286.35198
Robinson, James C.
2013
Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Zbl 1126.37008
Langa, J. A.; Robinson, J. C.; Rodríguez-Bernal, A.; Suárez, A.; Vidal-López, A.
2007
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces. Zbl 1163.54008
Robinson, James C.
2009
Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system. Zbl 1044.34009
Langa, José A.; Robinson, James C.; Suárez, Antonio
2003
Rigorous numerical verification of uniqueness and smoothness in a surface growth model. Zbl 1315.65092
Blömker, Dirk; Nolde, Christian; Robinson, James C.
2015
Energy equality for the 3D critical convective Brinkman-Forchheimer equations. Zbl 1379.35242
Hajduk, Karol W.; Robinson, James C.
2017
Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion. Zbl 1185.35119
Langa, José A.; Robinson, James C.; Rodríguez-Bernal, Aníbal; Suárez, Antonio
2009
Smooth attractors have zero “thickness”. Zbl 0971.37011
Friz, Peter K.; Robinson, James C.
1999
Inertial manifolds for the Kuramoto-Sivashinsky equation. Zbl 0941.35511
Robinson, James C.
1994
On the continuity of global attractors. Zbl 1356.37027
Hoang, Luan T.; Olson, Eric J.; Robinson, James C.
2015
Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values. Zbl 1076.35090
Friz, P. K.; Robinson, J. C.
2001
Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation. Zbl 1317.35206
McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2014
An a posteriori condition on the numerical approximations of the Navier-Stokes equations for the existence of a strong solution. Zbl 1235.76022
Dashti, Masoumeh; Robinson, James C.
2008
Pullback attractors for the non-autonomous 2D Navier-Stokes equations for minimally regular forcing. Zbl 1277.35064
García-Luengo, Julia; Marín-Rubio, Pedro; Real, José; Robinson, James C.
2014
Solutions of the 3D Navier-Stokes equations for initial data in $$\dot H^{1/2}$$: robustness of regularity and numerical verification of regularity for bounded sets of initial data in. Zbl 1310.35190
Marín-Rubio, Pedro; Robinson, James C.; Sadowski, Witold
2013
An introduction to ordinary differential equations. Zbl 1053.34001
Robinson, James C.
2004
Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data. Zbl 1155.35071
2008
Continuity of pullback and uniform attractors. Zbl 1383.37011
Hoang, Luan T.; Olson, Eric J.; Robinson, James C.
2018
Generalised Cantor sets and the dimension of products. Zbl 1371.28024
Olson, Eric J.; Robinson, James C.; Sharples, Nicholas
2016
Partial regularity for a surface growth model. Zbl 1408.35065
Ożański, Wojciech S.; Robinson, James C.
2019
The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius. Zbl 1294.76082
Dashti, Masoumeh; Robinson, James C.
2011
Nodal parametrisation of analytic attractors. Zbl 1153.37439
Friz, Peter K.; Kukavica, Igor; Robinson, James C.
2001
A concise proof of the ”geometric” construction of inertial manifolds. Zbl 1020.34509
Robinson, James C.
1995
Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. Zbl 1058.35045
Kukavica, Igor; Robinson, James C.
2004
Embedding of global attractors and their dynamics. Zbl 1250.37032
Pinto de Moura, Eleonora; Robinson, James C.; Sánchez-Gabites, J. J.
2011
A rigorous treatment of ‘experimental’ observations for the two-dimensional Navier-Stokes equations. Zbl 1013.35062
Robinson, James C.
2001
Lipschitz deviation and embeddings of global attractors. Zbl 1213.37112
Pinto de Moura, Eleonora; Robinson, James C.
2010
Strict inequality in the box-counting dimension product formulas. Zbl 1277.28014
Robinson, James C.; Sharples, Nicholas
2013
Inertial manifolds with and without delay. Zbl 0954.37037
Robinson, James C.
1999
Non-existence of local solutions for semilinear heat equations of Osgood type. Zbl 1319.35108
Laister, R.; Robinson, J. C.; Sierżȩga, M.
2013
A criterion for uniqueness of Lagrangian trajectories for weak solutions of the 3D Navier-Stokes equations. Zbl 1186.35146
2009
Well-posedness for the diffusive 3D Burgers equations with initial data in $$H^{1/2}$$. Zbl 1365.35079
Pooley, Benjamin C.; Robinson, James C.
2016
Computing inertial manifolds. Zbl 1032.34060
Robinson, James C.
2002
Inertial manifolds and the cone condition. Zbl 0787.34036
Robinson, James C.
1993
A local smoothness criterion for solutions of the 3D Navier-Stokes equations. Zbl 1296.35123
2014
A note on well-posedness of semilinear reaction-diffusion problem with singular initial data. Zbl 1227.35095
Robinson, James C.; Sierżȩga, Mikołaj
2012
A finite number of point observations which determine a non-autonomous fluid flow. Zbl 1193.37103
Langa, José A.; Robinson, James C.
2001
Pullback permanence in a non-autonomous competitive Lotka–Volterra model. Zbl 1027.35017
Langa, J. A.; Robinson, J. C.; Suárez, A.
2003
A coupled particle-continuum model: Well-posedness and the limit of zero radius. Zbl 1063.76106
Robinson, James C.
2004
Determining asymptotic behavior from the dynamics on attracting sets. Zbl 0933.34059
Langa, José A.; Robinson, James C.
1999
Orthogonal sequences and regularity of embeddings into finite-dimensional spaces. Zbl 1206.46023
Pinto de Moura, E.; Robinson, J. C.
2010
A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations. Zbl 1165.35424
Dashti, M.; Robinson, J. C.
2009
A topological time-delay embeddding theorem for infinite-dimensional cocycle dynamical systems. Zbl 1149.37011
Robinson, J. C.
2008
Regularity and singularity in the three-dimensional Navier-Stokes equations. Zbl 1244.35106
Robinson, James C.
2006
Arbitrarily accurate approximate inertial manifolds of fixed dimension. Zbl 1052.34509
Robinson, James C.
1997
Energy conservation for the Euler equations on $$\mathbb{T}^2 \times \mathbb{R}_+$$ for weak solutions defined without reference to the pressure. Zbl 1417.35104
Robinson, James C.; Rodrigo, José L.; Skipper, Jack W. D.
2018
Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. Zbl 1092.35514
Langa, José A.; Robinson, James C.; Suárez, Antonio
2005
A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations. Zbl 1372.35156
Laister, R.; Robinson, J. C.; Sierżęga, M.
2017
Some closure results for inertial manifolds. Zbl 0901.34053
Robinson, J. C.
1997
Finite-dimensional behavior in dissipative partial differential equations. Zbl 1055.35501
Robinson, J. C.
1995
Low dimensional attractors arise from forcing at small scales. Zbl 1040.35063
Robinson, James C.
2003
The regularity problem for the three-dimensional Navier-Stokes equations. Zbl 1387.35465
2009
Finite-dimensional global attractors in Banach spaces. Zbl 1215.35038
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2010
On finite-dimensional global attractors of homeomorphisms. Zbl 1362.37066
Robinson, James C.; Sánchez-Gabites, Jaime J.
2016
Lower bounds on blowing-up solutions of the three-dimensional Navier-Stokes equations in $$\dot H^{3/2}$$, $$\dot H^{5/2}$$, and $$\dot B^{5/2}_{2,1}$$. Zbl 1344.35081
McCormick, David S.; Olson, Eric J.; Robinson, James C.; Rodrigo, Jose L.; Vidal-López, Alejandro; Zhou, Yi
2016
Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Zbl 1321.34020
Robinson, James C.; Sharples, Nicholas
2013
Partial regularity for the 3D Navier-Stokes equations. Zbl 1442.35309
Robinson, James C.
2020
Partial regularity for a surface growth model. Zbl 1408.35065
Ożański, Wojciech S.; Robinson, James C.
2019
Embedding properties of sets with finite box-counting dimension. Zbl 1428.37020
Margaris, Alexandros; Robinson, James C.
2019
Continuity of pullback and uniform attractors. Zbl 1383.37011
Hoang, Luan T.; Olson, Eric J.; Robinson, James C.
2018
Energy conservation for the Euler equations on $$\mathbb{T}^2 \times \mathbb{R}_+$$ for weak solutions defined without reference to the pressure. Zbl 1417.35104
Robinson, James C.; Rodrigo, José L.; Skipper, Jack W. D.
2018
Optimal existence classes and nonlinear-like dynamics in the linear heat equation in $$\mathbb{R}^d$$. Zbl 1400.35151
Robinson, James C.; Rodríguez-Bernal, Aníbal
2018
Energy conservation in the 3D Euler equations on $${\mathbb T}^2 \times {\mathbb R}_+$$. Zbl 1408.35139
Robinson, James C.; Rodrigo, José L.; Skipper, Jack W. D.
2018
Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces. Zbl 1359.35150
Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2017
Energy equality for the 3D critical convective Brinkman-Forchheimer equations. Zbl 1379.35242
Hajduk, Karol W.; Robinson, James C.
2017
A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations. Zbl 1372.35156
Laister, R.; Robinson, J. C.; Sierżęga, M.
2017
The three-dimensional Navier-Stokes equations. Classical theory. Zbl 1358.35002
Robinson, James C.; Rodrigo, José L.; Sadowski, Witold
2016
Local existence for the non-resistive MHD equations in Besov spaces. Zbl 1333.35183
Chemin, Jean-Yves; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2016
A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Zbl 1349.35169
Laister, R.; Robinson, J. C.; Sierżȩga, M.; Vidal-López, A.
2016
Generalised Cantor sets and the dimension of products. Zbl 1371.28024
Olson, Eric J.; Robinson, James C.; Sharples, Nicholas
2016
Well-posedness for the diffusive 3D Burgers equations with initial data in $$H^{1/2}$$. Zbl 1365.35079
Pooley, Benjamin C.; Robinson, James C.
2016
On finite-dimensional global attractors of homeomorphisms. Zbl 1362.37066
Robinson, James C.; Sánchez-Gabites, Jaime J.
2016
Lower bounds on blowing-up solutions of the three-dimensional Navier-Stokes equations in $$\dot H^{3/2}$$, $$\dot H^{5/2}$$, and $$\dot B^{5/2}_{2,1}$$. Zbl 1344.35081
McCormick, David S.; Olson, Eric J.; Robinson, James C.; Rodrigo, Jose L.; Vidal-López, Alejandro; Zhou, Yi
2016
An Eulerian-Lagrangian form for the Euler equations in Sobolev spaces. Zbl 1359.76041
Pooley, Benjamin C.; Robinson, James C.
2016
On the Assouad dimension of self-similar sets with overlaps. Zbl 1317.28014
Fraser, J. M.; Henderson, A. M.; Olson, E. J.; Robinson, J. C.
2015
Non-autonomous dynamical systems. Zbl 1384.37024
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2015
Rigorous numerical verification of uniqueness and smoothness in a surface growth model. Zbl 1315.65092
Blömker, Dirk; Nolde, Christian; Robinson, James C.
2015
On the continuity of global attractors. Zbl 1356.37027
Hoang, Luan T.; Olson, Eric J.; Robinson, James C.
2015
A simple example concerning the upper box-counting dimension of a Cartesian product. Zbl 1384.28008
Olson, Eric J.; Robinson, James C.
2015
Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Zbl 1296.35142
Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2014
Invariant measures for non-autonomous dissipative dynamical systems. Zbl 1351.37076
Łukaszewicz, Grzegorz; Robinson, James C.
2014
A weak-$$L^p$$ Prodi-Serrin type regularity criterion for the Navier-Stokes equations. Zbl 1307.35186
Bosia, Stefano; Pata, Vittorino; Robinson, James C.
2014
Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation. Zbl 1317.35206
McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2014
Pullback attractors for the non-autonomous 2D Navier-Stokes equations for minimally regular forcing. Zbl 1277.35064
García-Luengo, Julia; Marín-Rubio, Pedro; Real, José; Robinson, James C.
2014
A local smoothness criterion for solutions of the 3D Navier-Stokes equations. Zbl 1296.35123
2014
Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains. (Non-existence de solutions locales pour les équations de la chaleur semi-linéaires de type Osgood dans des domaines bornés.) Zbl 1297.35114
Laister, Robert; Robinson, James C.; Sierżȩga, Mikolaj
2014
Log-Lipschitz continuity of the vector field on the attractor of certain parabolic equations. Zbl 1315.35038
De Moura, Eleonora Pinto; Robinson, James C.
2014
Log-Lipschitz embeddings of homogeneous sets with sharp logarithmic exponents and slicing products of balls. Zbl 1314.46029
Robinson, James C.
2014
Minimal periods for ordinary differential equations in strictly convex Banach spaces and explicit bounds for some $$L^p$$-spaces. Zbl 1287.34032
Nieuwenhuis, Michaela A. C.; Robinson, James C.; Steinerberger, Stefan
2014
Attractors for infinite-dimensional non-autonomous dynamical systems. Zbl 1263.37002
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2013
Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO. Zbl 1291.46029
McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2013
Supersolutions for a class of semilinear heat equations. Zbl 1334.35169
Robinson, James C.; Sierżęga, Mikołaj
2013
Attractors and finite-dimensional behaviour in the 2D Navier-Stokes equations. Zbl 1286.35198
Robinson, James C.
2013
Solutions of the 3D Navier-Stokes equations for initial data in $$\dot H^{1/2}$$: robustness of regularity and numerical verification of regularity for bounded sets of initial data in. Zbl 1310.35190
Marín-Rubio, Pedro; Robinson, James C.; Sadowski, Witold
2013
Strict inequality in the box-counting dimension product formulas. Zbl 1277.28014
Robinson, James C.; Sharples, Nicholas
2013
Non-existence of local solutions for semilinear heat equations of Osgood type. Zbl 1319.35108
Laister, R.; Robinson, J. C.; Sierżȩga, M.
2013
Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Zbl 1321.34020
Robinson, James C.; Sharples, Nicholas
2013
Minimal periods of semilinear evolution equations with Lipschitz nonlinearity revisited. Zbl 1284.34056
Robinson, James C.; Vidal-López, Alejandro
2013
Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation. Zbl 1282.35042
Carvalho, A. N.; Langa, J. A.; Robinson, J. C.
2012
Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces. Zbl 1425.76055
Robinson, James C.; Sadowski, Witold; Silva, Ricardo P.
2012
On the dimension of the singular set of solutions to the Navier-Stokes equations. Zbl 1233.35162
2012
A note on well-posedness of semilinear reaction-diffusion problem with singular initial data. Zbl 1227.35095
Robinson, James C.; Sierżȩga, Mikołaj
2012
Dimensions, embeddings, and attractors. Zbl 1222.37004
Robinson, James C.
2011
Invariant measures for dissipative systems and generalised Banach limits. Zbl 1230.37094
Łukaszewicz, Grzegorz; Real, José; Robinson, James C.
2011
The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius. Zbl 1294.76082
Dashti, Masoumeh; Robinson, James C.
2011
Embedding of global attractors and their dynamics. Zbl 1250.37032
Pinto de Moura, Eleonora; Robinson, James C.; Sánchez-Gabites, J. J.
2011
Almost bi-Lipschitz embeddings and almost homogeneous sets. Zbl 1197.54045
Olson, Eric J.; Robinson, James C.
2010
Lipschitz deviation and embeddings of global attractors. Zbl 1213.37112
Pinto de Moura, Eleonora; Robinson, James C.
2010
Orthogonal sequences and regularity of embeddings into finite-dimensional spaces. Zbl 1206.46023
Pinto de Moura, E.; Robinson, J. C.
2010
Finite-dimensional global attractors in Banach spaces. Zbl 1215.35038
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2010
Bayesian inverse problems for functions and applications to fluid mechanics. Zbl 1228.35269
Cotter, S. L.; Dashti, M.; Robinson, J. C.; Stuart, A. M.
2009
On the continuity of pullback attractors for evolution processes. Zbl 1175.37078
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2009
Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1173.35631
2009
Lower semicontinuity of attractors for non-autonomous dynamical systems. Zbl 1181.37016
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.
2009
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces. Zbl 1163.54008
Robinson, James C.
2009
Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion. Zbl 1185.35119
Langa, José A.; Robinson, James C.; Rodríguez-Bernal, Aníbal; Suárez, Antonio
2009
A criterion for uniqueness of Lagrangian trajectories for weak solutions of the 3D Navier-Stokes equations. Zbl 1186.35146
2009
A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations. Zbl 1165.35424
Dashti, M.; Robinson, J. C.
2009
The regularity problem for the three-dimensional Navier-Stokes equations. Zbl 1387.35465
2009
An a posteriori condition on the numerical approximations of the Navier-Stokes equations for the existence of a strong solution. Zbl 1235.76022
Dashti, Masoumeh; Robinson, James C.
2008
Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data. Zbl 1155.35071
2008
A topological time-delay embeddding theorem for infinite-dimensional cocycle dynamical systems. Zbl 1149.37011
Robinson, J. C.
2008
Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Zbl 1119.37023
Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.; Suárez, Antonio
2007
A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. Zbl 1144.81329
Chernyshenko, Sergei I.; Constantin, Peter; Robinson, James C.; Titi, Edriss S.
2007
The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C.
2007
The stability of attractors for non-autonomous perturbations of gradient-like systems. Zbl 1115.37064
Langa, José A.; Robinson, James C.; Suárez, Antonio; Vidal-López, Alejandro
2007
Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems. Zbl 1137.35009
Robinson, James C.; Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro
2007
Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations. Zbl 1120.35075
2007
Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Zbl 1126.37008
Langa, J. A.; Robinson, J. C.; Rodríguez-Bernal, A.; Suárez, A.; Vidal-López, A.
2007
Parametrization of global attractors, experimental observations, and turbulence. Zbl 1175.76041
Robinson, James C.
2007
Fractal dimension of a random invariant set. Zbl 1134.37364
Langa, José A.; Robinson, James C.
2006
Bifurcations in non-autonomous scalar equations. Zbl 1096.34026
Langa, J. A.; Robinson, J. C.; Suárez, A.
2006
Regularity and singularity in the three-dimensional Navier-Stokes equations. Zbl 1244.35106
Robinson, James C.
2006
Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Zbl 1087.34037
Robinson, James C.; Vidal-López, Alejandro
2006
A topological delay embedding theorem for infinite-dimensional dynamical systems. Zbl 1084.37063
Robinson, James C.
2005
Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. Zbl 1092.35514
Langa, José A.; Robinson, James C.; Suárez, Antonio
2005
Stabilisation of linear PDEs by Stratonovich noise. Zbl 1157.60332
Caraballo, Tomás; Robinson, James C.
2004
An introduction to ordinary differential equations. Zbl 1053.34001
Robinson, James C.
2004
Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. Zbl 1058.35045
Kukavica, Igor; Robinson, James C.
2004
A coupled particle-continuum model: Well-posedness and the limit of zero radius. Zbl 1063.76106
Robinson, James C.
2004
Stability of random attractors for a backwards Euler scheme. Zbl 1082.37056
Robinson, James C.
2004
A comparison between two theories for multi-valued semiflows and their asymptotic behaviour. Zbl 1053.47050
Caraballo, T.; Marín-Rubio, P.; Robinson, J. C.
2003
Attractors for the stochastic 3D Navier-Stokes equations. Zbl 1059.35100
Marín-Rubio, Pedro; Robinson, James C.
2003
Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system. Zbl 1044.34009
Langa, José A.; Robinson, James C.; Suárez, Antonio
2003
Pullback permanence in a non-autonomous competitive Lotka–Volterra model. Zbl 1027.35017
Langa, J. A.; Robinson, J. C.; Suárez, A.
2003
Low dimensional attractors arise from forcing at small scales. Zbl 1040.35063
Robinson, James C.
2003
Stability, instability, and bifurcation phenomena in non-autonomous differential equations. Zbl 1004.37032
Langa, José A.; Robinson, James C.; Suárez, Antonio
2002
Stability of random attractors under perturbation and approximation. Zbl 1020.37033
Robinson, James C.
2002
Computing inertial manifolds. Zbl 1032.34060
Robinson, James C.
2002
Constructing an elementary measure on a space of projections. Zbl 1189.53072
Friz, Peter K.; Robinson, James C.
2002
Infinite-dimensional dynamical systems. An introduction to dissipative parabolic PDEs and the theory of global attractors. Zbl 0980.35001
Robinson, James C.
2001
Introduction (to “From finite to infinite dimensional dynamical systems”). Zbl 1026.37500
Robinson, J. C.; Glendinning, P. A.
2001
A stochastic pitchfork bifurcation in a reaction-diffusion equation. Zbl 0996.60070
Caraballo, Tomás; Langa, José A.; Robinson, James C.
2001
Attractors for differential equations with variable delays. Zbl 0997.34073
Caraballo, Tomás; Langa, José A.; Robinson, James C.
2001
Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values. Zbl 1076.35090
Friz, P. K.; Robinson, J. C.
2001
Nodal parametrisation of analytic attractors. Zbl 1153.37439
Friz, Peter K.; Kukavica, Igor; Robinson, James C.
2001
...and 19 more Documents
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#### Cited by 1,396 Authors

 65 Robinson, James Cooper 49 Langa, Jose’ Antonio 44 Caraballo Garrido, Tomás 38 Kloeden, Peter Eris 34 Zhong, Chengkui 32 Li, Yangrong 31 Nolasco de Carvalho, Alexandre 29 Valero, José 28 Sun, Chunyou 26 Zhao, Caidi 23 Zhou, Shengfan 19 Marín-Rubio, Pedro 18 Cui, Hongyong 16 Duan, Jinqiao 15 Cung The Anh 15 Fraser, Jonathan MacDonald 15 Li, Desheng 15 Real Anguas, José 15 Titi, Edriss Saleh 15 Yang, Meihua 13 Łukaszewicz, Grzegorz 13 Wang, Bixiang 13 Yang, Xinguang 12 Simsen, Jacson 11 Kapustyan, Oleksiy V. 11 Obaya, Rafael 11 Olson, Eric J. 11 Sanjurjo, José M. R. 11 Wang, Yejuan 11 You, Yuncheng 11 Zelik, Sergey V. 10 Bortolan, Matheus Cheque 10 Kalita, Piotr 10 Kukavica, Igor 10 Nascimento, Marcelo Jose Dias 10 Stuart, Andrew M. 10 You, Bo 9 Bezerra, Flank David Morais 9 Bonotto, Everaldo M. 9 Mohan, Manil Thankamani 9 Pizzocchero, Livio 9 Pötzsche, Christian 9 Yin, Jinyan 9 Zhou, Feng 9 Zhu, Kaixuan 8 Barge Yáñez, Héctor 8 Blömker, Dirk 8 Foiaş, Ciprian Ilie 8 Freitas, Mirelson M. 8 García-Luengo, Julia 8 Li, Fang 8 Rasmussen, Martin 8 Rodrigo, José Luis 8 Schmalfuß, Björn 8 Wu, Jiahong 8 Xie, Yongqin 8 Zhao, Wenqiang 7 Anguiano, María 7 Colucci, Renato 7 Gess, Benjamin 7 Huang, Jianhua 7 Jiang, Zaihong 7 Li, Fuzhi 7 Lu, Kening 7 Morosi, Carlo 7 Rodríguez-Bernal, Aníbal 7 Suárez, Antonio 7 Tan, Wen 7 Wang, Renhai 7 Yang, Lu 6 Chekroun, Mickaël D. 6 Cheskidov, Alexey 6 Czaja, Radosław 6 Han, Xiaoying 6 Ju, Xuewei 6 Kasyanov, Pavlo O. 6 Larios, Adam 6 Li, Xin 6 Liu, Guowei 6 Ma, Qiaozhen 6 Ma, Shan 6 McCormick, David S. 6 Meng, Fengjuan 6 Ożański, Wojciech Sławomir 6 Sierżȩga, Mikołaj 6 Temam, Roger Meyer 6 Tran, Chuong V. 6 Vidal-López, Alejandro 6 Wang, Wei 6 Wang, Zhaojuan 6 Yan, Xingjie 6 Yu, Xinwei 5 Adrover, Alessandra 5 Arrieta, José M. 5 Cholewa, Jan W. 5 Gal, Ciprian Gheorghe Sorin 5 Giona, Massimiliano 5 Gu, Anhui 5 Guo, Boling 5 Ishige, Kazuhiro ...and 1,296 more Authors
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#### Cited in 257 Serials

 135 Journal of Differential Equations 81 Journal of Mathematical Analysis and Applications 81 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 62 Discrete and Continuous Dynamical Systems. Series B 43 Discrete and Continuous Dynamical Systems 35 Journal of Mathematical Physics 32 Physica D 32 Journal of Dynamics and Differential Equations 25 Communications on Pure and Applied Analysis 24 Nonlinear Analysis. Real World Applications 21 Nonlinearity 21 Journal of Mathematical Fluid Mechanics 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 19 Stochastics and Dynamics 18 Applied Mathematics and Computation 15 Archive for Rational Mechanics and Analysis 15 Communications in Mathematical Physics 14 Transactions of the American Mathematical Society 14 Applied Mathematics Letters 14 SIAM Journal on Mathematical Analysis 14 Abstract and Applied Analysis 13 Mathematical Methods in the Applied Sciences 12 Proceedings of the American Mathematical Society 11 Computers & Mathematics with Applications 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Journal of Nonlinear Science 11 SIAM Journal on Applied Dynamical Systems 10 Advances in Mathematics 10 Applied Mathematics and Optimization 10 Dynamical Systems 9 Applicable Analysis 9 Chaos, Solitons and Fractals 9 Discrete and Continuous Dynamical Systems. Series S 9 Journal of Applied Analysis and Computation 8 Quarterly of Applied Mathematics 8 Stochastic Analysis and Applications 8 Chaos 8 Boundary Value Problems 7 Journal of Statistical Physics 7 Automatica 7 Journal of Functional Analysis 7 Ergodic Theory and Dynamical Systems 7 Systems & Control Letters 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Set-Valued Analysis 7 Topological Methods in Nonlinear Analysis 7 Journal of Difference Equations and Applications 7 Discrete Dynamics in Nature and Society 7 Evolution Equations and Control Theory 6 Acta Mathematica Vietnamica 6 Journal of Computational and Applied Mathematics 6 Acta Applicandae Mathematicae 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Communications in Nonlinear Science and Numerical Simulation 6 Journal of Evolution Equations 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Set-Valued and Variational Analysis 5 Journal of Fluid Mechanics 5 Annales Polonici Mathematici 5 Asymptotic Analysis 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Vietnam Journal of Mathematics 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Science China. Mathematics 5 SIAM/ASA Journal on Uncertainty Quantification 4 BIT 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Mathematical Problems in Engineering 4 Differential Equations and Dynamical Systems 4 Annals of PDE 3 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 3 Mathematische Annalen 3 Mathematics and Computers in Simulation 3 Mathematische Zeitschrift 3 Numerische Mathematik 3 SIAM Journal on Numerical Analysis 3 Applied Mathematics and Mechanics. (English Edition) 3 Applied Numerical Mathematics 3 The Annals of Applied Probability 3 The Journal of Geometric Analysis 3 International Journal of Computer Mathematics 3 NoDEA. Nonlinear Differential Equations and Applications 3 Complexity 3 Nonlinear Dynamics 3 Revista Matemática Complutense 3 Advanced Nonlinear Studies 3 Advances in Difference Equations 3 Stochastic and Partial Differential Equations. Analysis and Computations 3 Journal of Fractal Geometry 3 Journal of Elliptic and Parabolic Equations 2 International Journal of Engineering Science 2 Inverse Problems 2 Rocky Mountain Journal of Mathematics 2 Mathematics of Computation 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Probability 2 Archiv der Mathematik 2 Indiana University Mathematics Journal 2 International Journal of Mathematics and Mathematical Sciences 2 Real Analysis Exchange ...and 157 more Serials
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#### Cited in 42 Fields

 981 Partial differential equations (35-XX) 540 Dynamical systems and ergodic theory (37-XX) 365 Fluid mechanics (76-XX) 180 Probability theory and stochastic processes (60-XX) 155 Ordinary differential equations (34-XX) 79 Numerical analysis (65-XX) 54 Systems theory; control (93-XX) 52 Measure and integration (28-XX) 51 Operator theory (47-XX) 48 Biology and other natural sciences (92-XX) 36 Mechanics of deformable solids (74-XX) 29 Functional analysis (46-XX) 29 Geophysics (86-XX) 24 Statistics (62-XX) 22 General topology (54-XX) 19 Statistical mechanics, structure of matter (82-XX) 16 Global analysis, analysis on manifolds (58-XX) 16 Classical thermodynamics, heat transfer (80-XX) 14 Real functions (26-XX) 14 Difference and functional equations (39-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 8 Integral equations (45-XX) 7 Mechanics of particles and systems (70-XX) 6 Manifolds and cell complexes (57-XX) 6 Computer science (68-XX) 5 Algebraic topology (55-XX) 5 Quantum theory (81-XX) 5 Information and communication theory, circuits (94-XX) 4 Functions of a complex variable (30-XX) 4 Differential geometry (53-XX) 4 Optics, electromagnetic theory (78-XX) 4 Operations research, mathematical programming (90-XX) 3 Number theory (11-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Convex and discrete geometry (52-XX) 1 Astronomy and astrophysics (85-XX)