Edit Profile (opens in new tab) Abels, Helmut Co-Author Distance Author ID: abels.helmut Published as: Abels, Helmut; Abels, H. Homepage: https://www.uni-regensburg.de/mathematik/mathematik-abels/startseite/index.html External Links: MGP Documents Indexed: 106 Publications since 2002, including 2 Books and 10 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 62 Co-Authors with 84 Joint Publications 1,245 Co-Co-Authors all top 5 Co-Authors 24 single-authored 16 Garcke, Harald 6 Terasawa, Yutaka 5 Moser, Maximilian 5 Pfeuffer, Christine 4 Liu, Yadong 4 Liu, Yuning 4 Weber, Josef 3 Grubb, Gerd 3 Grün, Günther 3 Kampmann, Johannes 3 Marquardt, Andreas 3 Mora, Maria Giovanna 3 Müller, Stefan 3 Schaubeck, Stefan 3 Wilke, Mathias 2 Ameismeier, Tobias 2 Arab, Nasrin 2 Bürger, Felicitas 2 Butz, Julia 2 Daube, Johannes 2 Depner, Daniel 2 Diening, Lars 2 Dolzmann, Georg 2 Fei, Mingwen 2 Kaßmann, Moritz 2 Kraus, Christiane 2 Lam, Kei Fong 2 Müller, Lars 1 Aland, Sebastian 1 Altenbach, Holm 1 Bosia, Stefano 1 Breit, Dominic 1 Disser, Karoline 1 Feireisl, Eduard 1 Fischer, Julian 1 Giorgini, Andrea 1 Grasselli, Maurizio 1 Haselböck, Jonas 1 Hurm, Christoph 1 Husseini, Ryad 1 Kaiser, Hans-Christoph 1 Krbec, Miroslav 1 Kröner, Dietmar 1 Lengeler, Daniel 1 Matioc, Bogdan-Vasile 1 Metzger, Stefan 1 Mielke, Alexander 1 Mokbel, Dominic 1 Nečasová, Šárka 1 Neira Jiménez, Carolina 1 Odenbach, Stefan 1 Platzer, Beate 1 Poiatti, Andrea 1 Rauchecker, Maximilian 1 Röger, Matthias 1 Schöttl, Andreas 1 Schumacher, Katrin 1 Stinner, Bjorn 1 Thomas, Marita 1 Wiegner, Michael 1 Wieners, Christian 1 Wood, Ian Geoffrey all top 5 Serials 6 SIAM Journal on Mathematical Analysis 5 Interfaces and Free Boundaries 5 Discrete and Continuous Dynamical Systems. Series S 4 Journal of Differential Equations 4 Journal of Mathematical Fluid Mechanics 4 Journal of Evolution Equations 3 Mathematische Nachrichten 3 Asymptotic Analysis 2 Archive for Rational Mechanics and Analysis 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 Mathematische Annalen 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 European Journal of Applied Mathematics 2 Communications in Partial Differential Equations 2 Advances in Differential Equations 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Communications in Mathematical Physics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Computational Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Arkiv för Matematik 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Indiana University Mathematics Journal 1 Integral Equations and Operator Theory 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Zeitschrift 1 Osaka Journal of Mathematics 1 Zeitschrift für Analysis und ihre Anwendungen 1 Differential and Integral Equations 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Communications in Analysis and Geometry 1 Calculus of Variations and Partial Differential Equations 1 The Journal of Fourier Analysis and Applications 1 Analysis (München) 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 Analysis and Applications (Singapore) 1 Journal of Function Spaces and Applications 1 GAMM-Mitteilungen 1 RIMS Kôkyûroku Bessatsu 1 Journal of Pseudo-Differential Operators and Applications 1 Advances in Nonlinear Analysis 1 Berichte aus der Mathematik 1 SN Partial Differential Equations and Applications all top 5 Fields 103 Partial differential equations (35-XX) 66 Fluid mechanics (76-XX) 18 Operator theory (47-XX) 13 Mechanics of deformable solids (74-XX) 9 Differential geometry (53-XX) 7 Classical thermodynamics, heat transfer (80-XX) 5 Probability theory and stochastic processes (60-XX) 5 Biology and other natural sciences (92-XX) 3 General and overarching topics; collections (00-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 2 Numerical analysis (65-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 85 Publications have been cited 1,440 times in 786 Documents Cited by ▼ Year ▼ Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342 Abels, Helmut; Garcke, Harald; Grün, Günther 203 2012 On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities. Zbl 1254.76158 Abels, Helmut 156 2009 Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy. Zbl 1121.35018 Abels, Helmut; Wilke, Mathias 81 2007 On a diffuse interface model for a two-phase flow of compressible viscous fluids. Zbl 1144.35041 Abels, Helmut; Feireisl, Eduard 66 2008 Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities. Zbl 1165.76050 Abels, Helmut 61 2009 Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Zbl 1273.76421 Abels, Helmut; Depner, Daniel; Garcke, Harald 55 2013 On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052 Abels, Helmut; Depner, Daniel; Garcke, Harald 45 2013 Pseudodifferential and singular integral operators. An introduction with applications. Zbl 1235.35001 Abels, Helmut 36 2012 Well-posedness of a fully coupled Navier-Stokes/\(\mathrm Q\)-tensor system with inhomogeneous boundary data. Zbl 1336.35283 Abels, Helmut; Dolzmann, Georg; Liu, Yuning 33 2014 On generalized solutions of two-phase flows for viscous incompressible fluids. Zbl 1124.35060 Abels, Helmut 32 2007 Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. Zbl 1181.35343 Abels, Helmut; Röger, Matthias 32 2009 On Stokes operators with variable viscosity in bounded and unbounded domains. Zbl 1172.35050 Abels, Helmut; Terasawa, Yutaka 30 2009 The initial-value problem for the Navier-Stokes equations with a free surface in \(L^q\)-Sobolev spaces. Zbl 1105.35072 Abels, Helmut 29 2005 Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system. Zbl 1167.76008 Abels, Helmut 29 2009 Cahn-Hilliard equation with nonlocal singular free energies. Zbl 1320.35083 Abels, Helmut; Bosia, Stefano; Grasselli, Maurizio 28 2015 Strong well-posedness of a diffuse interface model for a viscous, quasi-incompressible two-phase flow. Zbl 1333.76079 Abels, Helmut 27 2012 The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity. Zbl 1346.74110 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 25 2011 Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions. Zbl 1333.35174 Abels, Helmut; Dolzmann, Georg; Liu, Yuning 24 2016 The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Zbl 1196.47037 Abels, Helmut; Kassmann, Moritz 21 2009 On sharp interface limits for diffuse interface models for two-phase flows. Zbl 1319.76058 Abels, Helmut; Lengeler, Daniel 21 2014 Sharp interface limit for a Stokes/Allen-Cahn system. Zbl 1394.35343 Abels, Helmut; Liu, Yuning 21 2018 Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems. Zbl 1312.47019 Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey 19 2014 Reduced and generalized Stokes resolvent equations in asymptotically flat layers. II: \(H_\infty\)-calculus. Zbl 1083.35085 Abels, Helmut 18 2005 Weak solutions for a non-Newtonian diffuse interface model with different densities. Zbl 1354.35084 Abels, Helmut; Breit, Dominic 16 2016 Nonstationary Stokes system with variable viscosity in bounded and unbounded domains. Zbl 1191.76038 Abels, Helmut 16 2010 A phase-field model for fluid-structure interaction. Zbl 1415.74023 Mokbel, Dominic; Abels, Helmut; Aland, Sebastian 16 2018 Pseudodifferential boundary value problems with nonsmooth coefficients. Zbl 1087.35099 Abels, Helmut 15 2005 Reduced and generalized Stokes resolvent equations in asymptotically flat layers. I: Unique solvability. Zbl 1070.35020 Abels, Helmut 14 2005 Large time existence for thin vibrating plates. Zbl 1247.74019 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 13 2011 Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Zbl 1297.35177 Abels, Helmut; Diening, Lars; Terasawa, Yutaka 13 2014 Resolvent estimates for the Stokes operator on an infinite layer. Zbl 1212.35343 Abels, Helmut; Wiegner, Michael 12 2005 Well-posedness and qualitative behaviour of solutions for a two-phase Navier-Stokes-Mullins-Sekerka system. Zbl 1302.35457 Abels, Helmut; Wilke, Mathias 11 2013 An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control. Zbl 1119.47048 Abels, Helmut; Kassmann, Moritz 10 2007 Analysis of the diffuse domain approach for a bulk-surface coupled PDE system. Zbl 1326.35112 Abels, Helmut; Lam, Kei Fong; Stinner, Björn 10 2015 Characterization of non-smooth pseudodifferential operators. Zbl 1391.35442 Abels, Helmut; Pfeuffer, Christine 8 2018 Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions. Zbl 1117.35060 Abels, Helmut 8 2006 On the trace space of Sobolev space with a radial weight. Zbl 1169.46012 Abels, Helmut; Krbec, Miroslav; Schumacher, Katrin 8 2008 Bounded imaginary power and \(H_{\infty}\)-calculus of the Stokes operator in unbounded domains. Zbl 1109.35084 Abels, Helmut 8 2005 Boundedness of imaginary powers of the Stokes operator in an infinite layer. Zbl 1030.35131 Abels, Helmut 8 2002 Two-phase flow with surfactants: diffuse interface models and their analysis. Zbl 1391.76766 Abels, Helmut; Garcke, Harald; Lam, Kei Fong; Weber, Josef 7 2017 Bounded imaginary powers and \(H_\infty\)-calculus of the Stokes operator in two-dimensional exterior domains. Zbl 1091.35054 Abels, Helmut 7 2005 Stokes equations in asymptotically flat domains and the motion of a free surface. Zbl 1028.35117 Abels, Helmut 7 2003 Sharp interface limit for the Cahn-Larché system. Zbl 1320.35022 Abels, Helmut; Schaubeck, Stefan 7 2015 Sharp interface limits for diffuse interface models for two-phase flows of viscous incompressible fluids. Zbl 1391.76767 Abels, Helmut; Liu, Yuning; Schöttl, Andreas 6 2017 Sharp interface limit of a Stokes/Cahn-Hilliard system. I: Convergence result. Zbl 1490.76210 Abels, Helmut; Marquardt, Andreas 6 2021 (Non)-convergence of solutions of the convective Allen-Cahn equation. Zbl 1513.76158 Abels, Helmut 6 2022 Well-posedness of a Navier-Stokes/mean curvature flow system. Zbl 1401.35353 Abels, Helmut; Moser, Maximilian 6 2018 Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants. Zbl 1404.35340 Abels, Helmut; Garcke, Harald; Weber, Josef 6 2019 On the notion of generalized solutions of viscous incompressible two-phase flows. Zbl 1119.35042 Abels, Helmut 5 2007 Spectral invariance of non-smooth pseudo-differential operators. Zbl 1372.35388 Abels, Helmut; Pfeuffer, Christine 5 2016 Short time existence for the curve diffusion flow with a contact angle. Zbl 1426.53098 Abels, Helmut; Butz, Julia 5 2019 Convergence of the Allen-Cahn equation to the mean curvature flow with \(90^\circ\)-contact angle in 2D. Zbl 1430.35127 Abels, Helmut; Moser, Maximilian 5 2019 Fractional-order operators on nonsmooth domains. Zbl 1521.35064 Abels, Helmut; Grubb, Gerd 5 2023 Weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities and nonlocal free energies. Zbl 1454.35251 Abels, Helmut; Terasawa, Yutaka 5 2020 Sharp interface limit of a Stokes/Cahn-Hilliard system. II: Approximate solutions. Zbl 1470.76101 Abels, Helmut; Marquardt, Andreas 5 2021 Well-posedness of the Muskat problem in subcritical \(L_p\)-Sobolev spaces. Zbl 1504.35269 Abels, H.; Matioc, B.-V. 5 2022 Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension. Zbl 1335.53079 Abels, Helmut; Garcke, Harald; Müller, Lars 4 2016 Stability of spherical caps under the volume-preserving mean curvature flow with line tension. Zbl 1314.53115 Abels, Helmut; Garcke, Harald; Müller, Lars 4 2015 Nonconvergence of the capillary stress functional for solutions of the convective Cahn-Hilliard equation. Zbl 1371.35209 Abels, Helmut; Schaubeck, Stefan 4 2016 Local well-posedness of a quasi-incompressible two-phase flow. Zbl 1490.76226 Abels, Helmut; Weber, Josef 4 2021 Convergence of the Allen-Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to \(90^\circ\). Zbl 1485.35020 Abels, Helmut; Moser, Maximilian 4 2022 On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions. Zbl 1366.35006 Abels, Helmut; Arab, Nasrin; Garcke, Harald 3 2015 Short time existence for coupling of scaled mean curvature flow and diffusion. Zbl 1509.53097 Abels, Helmut; Bürger, Felicitas; Garcke, Harald 3 2023 Qualitative properties for a system coupling scaled mean curvature flow and diffusion. Zbl 1510.53103 Abels, Helmut; Bürger, Felicitas; Garcke, Harald 3 2023 Convergence of a nonlocal to a local diffuse interface model for two-phase flow with unmatched densities. Zbl 1513.76149 Abels, Helmut; Terasawa, Yutaka 3 2022 Well-posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact. Zbl 1475.35427 Abels, Helmut; Rauchecker, Maximilian; Wilke, Mathias 3 2021 Pressure reconstruction for weak solutions of the two-phase incompressible Navier-Stokes equations with surface tension. Zbl 1428.35270 Abels, Helmut; Daube, Johannes; Kraus, Christiane 3 2019 Diffuse interface models for incompressible two-phase flows with different densities. Zbl 1391.76765 Abels, Helmut; Garcke, Harald; Grün, Günther; Metzger, Stefan 2 2017 \(L_q\)-\(L_r\)-estimates for non-stationary Stokes equations in an aperture domain. Zbl 1027.35087 Abels, Helmut 2 2002 Non-homogeneous Navier-Stokes systems with order-parameter-dependent stresses. Zbl 1303.76008 Abels, Helmut; Terasawa, Yutaka 2 2010 Standard planar double bubbles are dynamically stable under surface diffusion flow. Zbl 1480.35006 Abels, Helmut; Arab, Nasrin; Garcke, Harald 2 2021 Sharp interface limit for a Navier-Stokes/Allen-Cahn system with different viscosities. Zbl 07733785 Abels, Helmut; Fei, Mingwen 2 2023 On a model for phase separation on biological membranes and its relation to the Ohta-Kawasaki equation. Zbl 1504.35167 Abels, H.; Kampmann, J. 2 2020 On a fluid-structure interaction problem for plaque growth. Zbl 1504.35656 Abels, Helmut; Liu, Yadong 2 2023 Fredholm property of non-smooth pseudodifferential operators. Zbl 1523.35313 Abels, Helmut; Pfeuffer, Christine 2 2020 Double obstacle limit for a Navier-Stokes/Cahn-Hilliard system. Zbl 1247.35098 Abels, Helmut 1 2011 Stokes equations in asymptotically flat layers. Zbl 1101.35344 Abels, Helmut 1 2005 Stationary solutions for a Navier-Stokes/Cahn-Hilliard system with singular free energies. Zbl 1338.35348 Abels, Helmut; Weber, Josef 1 2016 Nonsmooth pseudodifferential boundary value problems on manifolds. Zbl 1441.35267 Abels, Helmut; Jiménez, Carolina Neira 1 2019 A blow-up criterion for the curve diffusion flow with a contact angle. Zbl 1447.53083 Abels, Helmut; Butz, Julia 1 2020 On hypoellipticity of generators of Lévy processes. Zbl 1205.60094 Abels, Helmut; Husseini, Ryad 1 2010 Book review of: A. Miranville, The Cahn-Hilliard equation: recent advances and applications. Zbl 1456.00004 Abels, Helmut 1 2021 On a fluid-structure interaction problem for plaque growth: cylindrical domain. Zbl 1504.35573 Abels, Helmut; Liu, Yadong 1 2023 Large times existence for thin vibrating rods. Zbl 1509.35300 Abels, Helmut; Ameismeier, Tobias 1 2023 Convergence of thin vibrating rods to a linear beam equation. Zbl 1493.74053 Abels, Helmut; Ameismeier, Tobias 1 2022 Fractional-order operators on nonsmooth domains. Zbl 1521.35064 Abels, Helmut; Grubb, Gerd 5 2023 Short time existence for coupling of scaled mean curvature flow and diffusion. Zbl 1509.53097 Abels, Helmut; Bürger, Felicitas; Garcke, Harald 3 2023 Qualitative properties for a system coupling scaled mean curvature flow and diffusion. Zbl 1510.53103 Abels, Helmut; Bürger, Felicitas; Garcke, Harald 3 2023 Sharp interface limit for a Navier-Stokes/Allen-Cahn system with different viscosities. Zbl 07733785 Abels, Helmut; Fei, Mingwen 2 2023 On a fluid-structure interaction problem for plaque growth. Zbl 1504.35656 Abels, Helmut; Liu, Yadong 2 2023 On a fluid-structure interaction problem for plaque growth: cylindrical domain. Zbl 1504.35573 Abels, Helmut; Liu, Yadong 1 2023 Large times existence for thin vibrating rods. Zbl 1509.35300 Abels, Helmut; Ameismeier, Tobias 1 2023 (Non)-convergence of solutions of the convective Allen-Cahn equation. Zbl 1513.76158 Abels, Helmut 6 2022 Well-posedness of the Muskat problem in subcritical \(L_p\)-Sobolev spaces. Zbl 1504.35269 Abels, H.; Matioc, B.-V. 5 2022 Convergence of the Allen-Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to \(90^\circ\). Zbl 1485.35020 Abels, Helmut; Moser, Maximilian 4 2022 Convergence of a nonlocal to a local diffuse interface model for two-phase flow with unmatched densities. Zbl 1513.76149 Abels, Helmut; Terasawa, Yutaka 3 2022 Convergence of thin vibrating rods to a linear beam equation. Zbl 1493.74053 Abels, Helmut; Ameismeier, Tobias 1 2022 Sharp interface limit of a Stokes/Cahn-Hilliard system. I: Convergence result. Zbl 1490.76210 Abels, Helmut; Marquardt, Andreas 6 2021 Sharp interface limit of a Stokes/Cahn-Hilliard system. II: Approximate solutions. Zbl 1470.76101 Abels, Helmut; Marquardt, Andreas 5 2021 Local well-posedness of a quasi-incompressible two-phase flow. Zbl 1490.76226 Abels, Helmut; Weber, Josef 4 2021 Well-posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact. Zbl 1475.35427 Abels, Helmut; Rauchecker, Maximilian; Wilke, Mathias 3 2021 Standard planar double bubbles are dynamically stable under surface diffusion flow. Zbl 1480.35006 Abels, Helmut; Arab, Nasrin; Garcke, Harald 2 2021 Book review of: A. Miranville, The Cahn-Hilliard equation: recent advances and applications. Zbl 1456.00004 Abels, Helmut 1 2021 Weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities and nonlocal free energies. Zbl 1454.35251 Abels, Helmut; Terasawa, Yutaka 5 2020 On a model for phase separation on biological membranes and its relation to the Ohta-Kawasaki equation. Zbl 1504.35167 Abels, H.; Kampmann, J. 2 2020 Fredholm property of non-smooth pseudodifferential operators. Zbl 1523.35313 Abels, Helmut; Pfeuffer, Christine 2 2020 A blow-up criterion for the curve diffusion flow with a contact angle. Zbl 1447.53083 Abels, Helmut; Butz, Julia 1 2020 Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants. Zbl 1404.35340 Abels, Helmut; Garcke, Harald; Weber, Josef 6 2019 Short time existence for the curve diffusion flow with a contact angle. Zbl 1426.53098 Abels, Helmut; Butz, Julia 5 2019 Convergence of the Allen-Cahn equation to the mean curvature flow with \(90^\circ\)-contact angle in 2D. Zbl 1430.35127 Abels, Helmut; Moser, Maximilian 5 2019 Pressure reconstruction for weak solutions of the two-phase incompressible Navier-Stokes equations with surface tension. Zbl 1428.35270 Abels, Helmut; Daube, Johannes; Kraus, Christiane 3 2019 Nonsmooth pseudodifferential boundary value problems on manifolds. Zbl 1441.35267 Abels, Helmut; Jiménez, Carolina Neira 1 2019 Sharp interface limit for a Stokes/Allen-Cahn system. Zbl 1394.35343 Abels, Helmut; Liu, Yuning 21 2018 A phase-field model for fluid-structure interaction. Zbl 1415.74023 Mokbel, Dominic; Abels, Helmut; Aland, Sebastian 16 2018 Characterization of non-smooth pseudodifferential operators. Zbl 1391.35442 Abels, Helmut; Pfeuffer, Christine 8 2018 Well-posedness of a Navier-Stokes/mean curvature flow system. Zbl 1401.35353 Abels, Helmut; Moser, Maximilian 6 2018 Two-phase flow with surfactants: diffuse interface models and their analysis. Zbl 1391.76766 Abels, Helmut; Garcke, Harald; Lam, Kei Fong; Weber, Josef 7 2017 Sharp interface limits for diffuse interface models for two-phase flows of viscous incompressible fluids. Zbl 1391.76767 Abels, Helmut; Liu, Yuning; Schöttl, Andreas 6 2017 Diffuse interface models for incompressible two-phase flows with different densities. Zbl 1391.76765 Abels, Helmut; Garcke, Harald; Grün, Günther; Metzger, Stefan 2 2017 Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions. Zbl 1333.35174 Abels, Helmut; Dolzmann, Georg; Liu, Yuning 24 2016 Weak solutions for a non-Newtonian diffuse interface model with different densities. Zbl 1354.35084 Abels, Helmut; Breit, Dominic 16 2016 Spectral invariance of non-smooth pseudo-differential operators. Zbl 1372.35388 Abels, Helmut; Pfeuffer, Christine 5 2016 Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension. Zbl 1335.53079 Abels, Helmut; Garcke, Harald; Müller, Lars 4 2016 Nonconvergence of the capillary stress functional for solutions of the convective Cahn-Hilliard equation. Zbl 1371.35209 Abels, Helmut; Schaubeck, Stefan 4 2016 Stationary solutions for a Navier-Stokes/Cahn-Hilliard system with singular free energies. Zbl 1338.35348 Abels, Helmut; Weber, Josef 1 2016 Cahn-Hilliard equation with nonlocal singular free energies. Zbl 1320.35083 Abels, Helmut; Bosia, Stefano; Grasselli, Maurizio 28 2015 Analysis of the diffuse domain approach for a bulk-surface coupled PDE system. Zbl 1326.35112 Abels, Helmut; Lam, Kei Fong; Stinner, Björn 10 2015 Sharp interface limit for the Cahn-Larché system. Zbl 1320.35022 Abels, Helmut; Schaubeck, Stefan 7 2015 Stability of spherical caps under the volume-preserving mean curvature flow with line tension. Zbl 1314.53115 Abels, Helmut; Garcke, Harald; Müller, Lars 4 2015 On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions. Zbl 1366.35006 Abels, Helmut; Arab, Nasrin; Garcke, Harald 3 2015 Well-posedness of a fully coupled Navier-Stokes/\(\mathrm Q\)-tensor system with inhomogeneous boundary data. Zbl 1336.35283 Abels, Helmut; Dolzmann, Georg; Liu, Yuning 33 2014 On sharp interface limits for diffuse interface models for two-phase flows. Zbl 1319.76058 Abels, Helmut; Lengeler, Daniel 21 2014 Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems. Zbl 1312.47019 Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey 19 2014 Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Zbl 1297.35177 Abels, Helmut; Diening, Lars; Terasawa, Yutaka 13 2014 Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Zbl 1273.76421 Abels, Helmut; Depner, Daniel; Garcke, Harald 55 2013 On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052 Abels, Helmut; Depner, Daniel; Garcke, Harald 45 2013 Well-posedness and qualitative behaviour of solutions for a two-phase Navier-Stokes-Mullins-Sekerka system. Zbl 1302.35457 Abels, Helmut; Wilke, Mathias 11 2013 Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342 Abels, Helmut; Garcke, Harald; Grün, Günther 203 2012 Pseudodifferential and singular integral operators. An introduction with applications. Zbl 1235.35001 Abels, Helmut 36 2012 Strong well-posedness of a diffuse interface model for a viscous, quasi-incompressible two-phase flow. Zbl 1333.76079 Abels, Helmut 27 2012 The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity. Zbl 1346.74110 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 25 2011 Large time existence for thin vibrating plates. Zbl 1247.74019 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 13 2011 Double obstacle limit for a Navier-Stokes/Cahn-Hilliard system. Zbl 1247.35098 Abels, Helmut 1 2011 Nonstationary Stokes system with variable viscosity in bounded and unbounded domains. Zbl 1191.76038 Abels, Helmut 16 2010 Non-homogeneous Navier-Stokes systems with order-parameter-dependent stresses. Zbl 1303.76008 Abels, Helmut; Terasawa, Yutaka 2 2010 On hypoellipticity of generators of Lévy processes. Zbl 1205.60094 Abels, Helmut; Husseini, Ryad 1 2010 On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities. Zbl 1254.76158 Abels, Helmut 156 2009 Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities. Zbl 1165.76050 Abels, Helmut 61 2009 Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. Zbl 1181.35343 Abels, Helmut; Röger, Matthias 32 2009 On Stokes operators with variable viscosity in bounded and unbounded domains. Zbl 1172.35050 Abels, Helmut; Terasawa, Yutaka 30 2009 Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system. Zbl 1167.76008 Abels, Helmut 29 2009 The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Zbl 1196.47037 Abels, Helmut; Kassmann, Moritz 21 2009 On a diffuse interface model for a two-phase flow of compressible viscous fluids. Zbl 1144.35041 Abels, Helmut; Feireisl, Eduard 66 2008 On the trace space of Sobolev space with a radial weight. Zbl 1169.46012 Abels, Helmut; Krbec, Miroslav; Schumacher, Katrin 8 2008 Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy. Zbl 1121.35018 Abels, Helmut; Wilke, Mathias 81 2007 On generalized solutions of two-phase flows for viscous incompressible fluids. Zbl 1124.35060 Abels, Helmut 32 2007 An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control. Zbl 1119.47048 Abels, Helmut; Kassmann, Moritz 10 2007 On the notion of generalized solutions of viscous incompressible two-phase flows. Zbl 1119.35042 Abels, Helmut 5 2007 Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions. Zbl 1117.35060 Abels, Helmut 8 2006 The initial-value problem for the Navier-Stokes equations with a free surface in \(L^q\)-Sobolev spaces. Zbl 1105.35072 Abels, Helmut 29 2005 Reduced and generalized Stokes resolvent equations in asymptotically flat layers. II: \(H_\infty\)-calculus. Zbl 1083.35085 Abels, Helmut 18 2005 Pseudodifferential boundary value problems with nonsmooth coefficients. Zbl 1087.35099 Abels, Helmut 15 2005 Reduced and generalized Stokes resolvent equations in asymptotically flat layers. I: Unique solvability. Zbl 1070.35020 Abels, Helmut 14 2005 Resolvent estimates for the Stokes operator on an infinite layer. Zbl 1212.35343 Abels, Helmut; Wiegner, Michael 12 2005 Bounded imaginary power and \(H_{\infty}\)-calculus of the Stokes operator in unbounded domains. Zbl 1109.35084 Abels, Helmut 8 2005 Bounded imaginary powers and \(H_\infty\)-calculus of the Stokes operator in two-dimensional exterior domains. Zbl 1091.35054 Abels, Helmut 7 2005 Stokes equations in asymptotically flat layers. Zbl 1101.35344 Abels, Helmut 1 2005 Stokes equations in asymptotically flat domains and the motion of a free surface. Zbl 1028.35117 Abels, Helmut 7 2003 Boundedness of imaginary powers of the Stokes operator in an infinite layer. Zbl 1030.35131 Abels, Helmut 8 2002 \(L_q\)-\(L_r\)-estimates for non-stationary Stokes equations in an aperture domain. Zbl 1027.35087 Abels, Helmut 2 2002 all cited Publications top 5 cited Publications all top 5 Cited by 958 Authors 54 Abels, Helmut 34 Grasselli, Maurizio 33 Garcke, Harald 22 Wu, Hao 20 Gal, Ciprian Gheorghe Sorin 17 Giorgini, Andrea 13 Miranville, Alain M. 13 Tachim Medjo, Theodore 11 Dong, Suchuan 11 Lam, Kei Fong 10 Nürnberg, Robert 10 Rocca, Elisabetta 10 Shibata, Yoshihiro 9 Frigeri, Sergio 9 Grubb, Gerd 9 Kahle, Christian 9 Knopf, Patrik 9 Liu, Chun 9 Schimperna, Giulio 9 Yang, Xiaofeng 8 Sprekels, Jürgen 8 Van Brummelen, Harald 8 Wise, Steven M. 7 Colli, Pierluigi 7 Feireisl, Eduard 7 Han, Daozhi 7 Liu, Yuning 7 Lowengrub, John Samuel 7 Metzger, Stefan 7 Poiatti, Andrea 7 Wang, Xiaoming 6 Aland, Sebastian 6 Behrndt, Jussi 6 Davoli, Elisa 6 Giga, Yoshikazu 6 Gilardi, Gianni 6 Guo, Zhenlin 6 Hintermüller, Michael 6 Hinze, Michael 6 Huang, Ziyang 6 Keil, Tobias 6 Kou, Jisheng 6 Lin, Ping 6 Matioc, Bogdan-Vasile 6 Nochetto, Ricardo Horacio 6 Scarpa, Luca 6 Temam, Roger Meyer 6 Wang, Cheng 6 Yang, Zhiguo 5 Ardekani, Arezoo M. 5 Chen, Wenbin 5 Deugoue, Gabriel 5 Ding, Shijin 5 Ebenbeck, Matthias 5 Geissert, Matthias 5 Grün, Günther 5 Hieber, Matthias 5 Kotschote, Matthias 5 Li, Yinghua 5 Lin, Guang 5 Moser, Maximilian 5 Saito, Hirokazu 5 Shimizu, Senjo 5 Terasawa, Yutaka 5 Vojnović, Ivana 5 Wang, Wei 5 Zhao, Jia 5 Zhao, Xiaopeng 4 Brunk, Aaron 4 Chen, Chuanjun 4 Chen, Yazhou 4 Di Primio, Andrea 4 Fei, Mingwen 4 Giesselmann, Jan 4 Gómez, Héctor J. 4 Kaßmann, Moritz 4 Knabner, Peter 4 Liang, Zhilei 4 Liero, Matthias 4 Liu, Qiao 4 Lukáčová-Medviďová, Mária 4 Maekawa, Yasunori 4 Miura, Hideyuki 4 Mora, Maria Giovanna 4 Münch, Andreas 4 Petcu, Madalina 4 Saal, Jürgen 4 Shokrpour Roudbari, Mahnaz 4 Sun, Shuyu 4 Wang, Qi 4 Weber, Josef 4 Wilke, Mathias 4 Xu, Xiang 4 You, Bo 4 Zhang, Zhifei 3 Abe, Ken 3 Aid, Omar Farouk 3 Balashov, Vladislav 3 Bänsch, Eberhard 3 Barrett, John William ...and 858 more Authors all top 5 Cited in 184 Serials 51 Journal of Computational Physics 46 Journal of Differential Equations 28 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 28 Journal of Mathematical Fluid Mechanics 25 Journal of Mathematical Analysis and Applications 24 SIAM Journal on Mathematical Analysis 20 Computer Methods in Applied Mechanics and Engineering 19 Archive for Rational Mechanics and Analysis 15 Journal of Scientific Computing 13 Mathematical Methods in the Applied Sciences 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Discrete and Continuous Dynamical Systems. Series S 12 Journal of Functional Analysis 11 Discrete and Continuous Dynamical Systems 10 Computers & Mathematics with Applications 10 Journal of Nonlinear Science 10 Nonlinear Analysis. Real World Applications 10 Communications on Pure and Applied Analysis 9 Mathematische Nachrichten 9 Calculus of Variations and Partial Differential Equations 9 NoDEA. 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Mathematics 3 Advances in Nonlinear Analysis 2 Communications in Mathematical Physics 2 Computer Physics Communications 2 International Journal of Engineering Science 2 Inverse Problems 2 Applied Mathematics and Computation 2 Archiv der Mathematik 2 BIT 2 Czechoslovak Mathematical Journal 2 International Journal for Numerical Methods in Engineering 2 Numerische Mathematik 2 Osaka Journal of Mathematics 2 Continuum Mechanics and Thermodynamics 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Advances in Computational Mathematics 2 The Journal of Fourier Analysis and Applications 2 Annals of Mathematics. Second Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Annales Henri Poincaré 2 Portugaliae Mathematica. Nova Série 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Stochastics and Dynamics 2 Milan Journal of Mathematics 2 Analysis and Applications (Singapore) 2 Journal of Hyperbolic Differential Equations 2 Mediterranean Journal of Mathematics 2 Oberwolfach Reports 2 Boundary Value Problems 2 Complex Variables and Elliptic Equations 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 AIMS Mathematics 2 Journal of Computational Physics: X 1 Communications on Pure and Applied Mathematics 1 Journal of Statistical Physics 1 Mathematical Notes ...and 84 more Serials all top 5 Cited in 37 Fields 607 Partial differential equations (35-XX) 454 Fluid mechanics (76-XX) 159 Numerical analysis (65-XX) 74 Mechanics of deformable solids (74-XX) 66 Operator theory (47-XX) 43 Statistical mechanics, structure of matter (82-XX) 42 Biology and other natural sciences (92-XX) 41 Classical thermodynamics, heat transfer (80-XX) 39 Probability theory and stochastic processes (60-XX) 37 Calculus of variations and optimal control; optimization (49-XX) 32 Dynamical systems and ergodic theory (37-XX) 26 Functional analysis (46-XX) 21 Integral equations (45-XX) 20 Differential geometry (53-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 17 Geophysics (86-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Real functions (26-XX) 7 Systems theory; control (93-XX) 5 Ordinary differential equations (34-XX) 5 Optics, electromagnetic theory (78-XX) 5 Quantum theory (81-XX) 4 Measure and integration (28-XX) 4 Operations research, mathematical programming (90-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Potential theory (31-XX) 3 Approximations and expansions (41-XX) 3 Integral transforms, operational calculus (44-XX) 2 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year