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Helmut Abels
Faculty of mathematics
University of Regensburg
Universitätsstraße 31
D-93053 Regensburg
Germany

Office: M 110
Phone: ++49 (0)941 943 4288
Fax: ++49 (0)941 943 3263
e-mail: helmut.abels"at"mathematik.uni-regensburg.de
Secratary: Karin Zirngibl, Office M 218, Tel. ++49 (0) 941 943 2390

Helmut Abels


Short vita

Since August 2009 Professor for applied mathematics at the Faculty of Mathematics, University of Regensburg
Apr 2009 - Jul 2009 Temporary position of a W2-professor (German: "Professurvertretung") at the Faculty of Mathematics, University of Regensburg
Sep 2008 Habilitation at the Department of Mathematics and Computer Sciences, University of Leipzig
Oct 2007 - Mar 2008 Temporary position of a W2-professor (German: "Professurvertretung") at the Institute of Applied Mathematics at the Univerity of Bonn
Nov 2004 - Jul 2009 Scientific Assistant at the Max Planck Institute for Mathematics in Science, Leipzig (on leave during Oct 2007 - Mar 2008, Apr 2009 - Jul 2009)
May 2003 PhD in mathematics, Darmstadt University of Technology
Aug 2001 - Mar 2002 Scientific work at the mathematical department of the University of Copenhagen, Denmark, (supported by DAAD)
Sep 2000 - Oct 2004 Scientific assistant at the Department of Mathematics, Darmstadt University of Technology
Sep 2000 Diploma in mathematics
Apr 1996- Sep 2000 Studies in mathematics (major) and computer science (minor), Darmstadt University of Technology

Research interests

Partial differential equations and mathematical fluid mechanics; in particular Navier-Stokes equations and other models for viscous fluids
Free boundary value problems, phase separation and phase transition, diffuse interface models for free boundary value problems
Pseudodifferential boundary value problems and pseudodifferential operators with non-smooth coefficients
Regularity of solutions of elliptic and parabolic systems

Teaching material

  • Lecture notes to the course on pseudodifferential operators, autumn term 2003/04, TU Darmstadt: PsDOSkript.ps

List of publications

PhD thesis

"Stokes Equations in Asymptotically Flat Domains and the Motion of a Free Surface", Dissertation, TU Darmstadt, Shaker Verlag, Aachen, 2003.

Habilitation thesis

"Diffuse Interface Models for Two-Phase Flows of Viscous, Incompressible Fluids"

Books

  1. "Pseudodifferential and Singular Integral Operators", Graduate Lecture, DeGruyter, 2011

Journal articles

  1. "Lq-Lr-estimates for non-stationary Stokes equations in an aperture domain", Z. Anal. Anwend. 21, No. 1, pp. 159-178, 2002.
  2. "Bounded imaginary powers of the Stokes operator in an infinite layer", J. Evol. Eq. 2, pp. 439-457, 2002
  3. "Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions", Math. Nachr. 279, No. 4, pp. 1-17, 2006
  4. "Reduced and generalized Stokes resolvent equations in asymptotically flat layers, part I: unique solvability", J. Math. Fluid Mech. 7 No. 2, pp. 201-222, 2005
  5. "Reduced and generalized Stokes resolvent equations in asymptotically flat layers, part II: Hinfty-calculus", J. Math. Fluid Mech. 7 No. 2, pp. 223-260, 2005
  6. "The initial value problem for the Navier-Stokes equations with a free surface in Lq-Sobolev spaces", Adv. Diff. Eq. 10. No. 1, pp. 45-64, 2005.
  7. "Pseudodifferential boundary value problems with non-smooth coeffficients", Comm. Part. Diff. Eq. 30, pp. 1463-1503, 2005
  8. "Bounded imaginary powers and Hinfty-calculus of the Stokes operator in two-dimensional exterior domains", Math. Z. 251 No. 3, pp. 589-605, 2005
  9. "Resolvent estimates for the Stokes operator on an infinite layer" with M. Wiegner, Diff. Int. Eq. 18 No. 10, pp. 1081-1110, 2005
  10. "On generalized solutions of two-phase flows for viscous incompressible fluids", Interfaces Free Bound. 9 No. 1, pp. 31-65, 2007
  11. "An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control" with M. Kassmann, J. Diff. Eq. 236 No. 1, pp. 29-56, 2007
  12. "Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy", Nonlinear Anal. 67 No. 11, pp. 3176-3193, 2007
  13. "On the trace space of a Sobolev space with a radial weight" with M. Krbec and K. Schumacher, J. Funct. Spaces Appl. 6, No. 3, 259-276 ,2008
  14. "On a diffuse interface model for a two-phase flow of compressible viscous fluids" with E. Feireisl, Indiana Univ. Math. J. 57 No. 2, pp. 659-698, 2008
  15. "On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities", Arch. Rational Mech. Anal. 194, No. 2, 463-506, 2009, DOI 10.1007/s00205-008-0160-2
  16. "On hypoellipticity of generators of Levy processes" with R. Husseini, Ark. Mat. 48 No. 2, 2010, pp. 231-242 DOI 10.1007/s00205-008-0160-2
  17. "On Stokes operators with variable viscosity in bounded and unbounded domains" with Y. Terasawa, Math. Ann. 344, No. 2, pp. 381-429 , 2009 DOI 10.1007/s00208-008-0311-7
  18. "The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels" with M. Kassmann, Osaka J. Math. 46, pp. 1-23, 2009
  19. "Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities", Comm. Math. Phys. Vol. 289, No. 1, pp. 45-73, 2009
  20. "Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids" with M. Röger, Annales de l'Institut Henri Poincare (C) Non Linear Analysis Vol. 26, pp. 2403-2424, 2009, DOI 10.1016/j.anihpc.2009.06.002
  21. "Nonstationary Stokes system with variable viscosity in bounded and unbounded domains", Discrete Contin. Dyn. Syst. Ser. S (Special volume in honour of V.A. Solonnikov) Vol. 3, No. 2, pp. 141-157, 2010, doi:10.3934/dcdss.2010.3.141
  22. "Non-homogeneous Navier-Stokes systems with order-parameter dependent stresses" with Y. Terasawa, Math. Methods Appl. Sci., Vol. 33., No. 13, pp. 1532-1544, 2010
  23. "The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity" with M.G. Mora and S. Müller, Calc. Var., Vol. 41, No. 1-2, pp. 241-259, 2011 DOI: 10.1007/s00526-010-0360-0
  24. "Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities" with H. Garcke and G. Grün, Mathematical Models and Methods in Applied Sciences, Vol. 22, No. 3, 1150013 (40 pages), 2012; Preprint: arXiv:/1104.1336,
  25. "Large time existence for thin vibrating plates" with M.G. Mora and S. Müller, Comm. Partial Differential Equations 36, pp. 2062-2102, 2011
  26. "Strong Well-Posedness of a Diffuse Interface Model for a Viscous, Quasi-Incompressible Two-Phase Flow", SIAM J. Math. Anal. 44, No.1, pp. 316-340, 2012; DOI: 10.1137/110829246, Preprint.
  27. "Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities" with D. Depner and H. Garcke, J. Math. Fluid Mech., Vol. 15, No. 3, pp. 453-480, 2013, Preprint arXiv:/1111.2493
  28. "Well-Posedness and Qualitative Behaviour of Solutions for a Two-Phase Navier-Stokes-Mullins-Sekerka System" with M. Wilke, Interfaces Free Bound., Vol. 15, No. 1, pp. 39–75, 2013 DOI: 10.4171/IFB/294; Preprint, arXiv:/1201.0179.
  29. "On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility" with D. Depner and H. Garcke, Annales de l'Institut Henri Poincare (C) Non Linear Analysis Ann. Vol. 30, No. 6, pp. 1175-1190, 2013 ; Preprint, arXiv:/1210.1011.
  30. "Existence of Weak Solutions for a Diffuse Interface Model of Non-Newtonian Two-Phase Flows" with L. Diening and Y. Terasawa, Nonlinear Analysis Series B: Real World Applications, Vol. 15, pp. 149–157, 2014; Preprint: arXiv:/1302.3107.
  31. "Extension theory and Krein-type resolvent formulas for nonsmooth boundary value problems" with G. Grubb and I. G. Wood, Journal of Functional Analysis, Vol. 266, No. 7, pp. 4037–4100; Preprint, arXiv:1008.3281
  32. "Cahn-Hilliard Equation with Nonlocal Singular Free Energies" with S. Bosia and M. Grasselli, accepted for publication in Annali di Matematica Pura ed Applicata; Preprint, arXiv:1311.3642/.
  33. Appendix to "Spectral Asymptotics for Nonsmooth Singular Green Operators" by G. Grubb, Communications in Partial Differential Equations , Vol. 39, pp. 530–573, 2014; Preprint, arXiv:1205.0094/.
  34. "On Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows" with D. Lengeler, Interfaces Free Bound. Vol. 16, No. 3, pp. 395–-418, 2014 ; Preprint, arXiv:/1212.5582.
  35. "Well-posedness of a fully-coupled Navier-Stokes/Q-tensor system with inhomogeneous boundary data" with G. Dolzmann and Y. Liu, SIAM J. Math. Anal., Vol. 46, No. 4, pp. 3050–3077; preprint, arXiv:1311.3443/.
  36. "Sharp Interface Limit for the Cahn-Larche System" with S. Schaubeck, Asymptotic Analysis, Vol. 91, pp. 283-–340, 2015; preprint: arXiv:1403.1151/
  37. "Classical Solutions for a Modified Hele-Shaw Model with Elasticity" with S. Schaubeck, Z. Angew. Math. Mech., pp. 1–-17, 2015.
  38. "Stability of Spherical Caps under the Volume-Preserving Mean Curvature Flow with Line Tension" with H. Garcke and L. Müller, Nonlinear Analysis, Vol. 117, pp. 8-–37, 2015; preprint arXiv:/1403.1139
  39. "On convergence of solutions to equilibria for fully nonlinear parabolic problems with nonlinear boundary conditions" with N. Arab and H. Garcke, J. Evol. Eq., 2015, DOI: 10.1007/s00028-015-0287-1; Preprint arXiv:/1403.4526
  40. "Local Well-Posedness for Volume-Preserving Mean Curvature and Willmore Flows with Line Tension" with H. Garcke and L. Müller to appear in Math. Nachr.; Preprint arXiv:1403.1132/
  41. "Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions" with G. Dolzmann and Y. Liu, accepted for publication in Adv. Diff. Eq.; Preprint arXiv:1312.5988/.
  42. "Analysis of the diffuse domain approach for a bulk-surface coupled PDE system" with Kei Fong Lam, Björn Stinner, accepted for publication in SIAM J. Math. Anal.; Preprint arXiv:1502.04902/.

Preprints, submitted

  1. "Standard Planar Double Bubbles are Stable under Surface Diffusion Flow" with N. Arab and H. Garcke, Preprint arXiv:/1505.02979
  2. "Weak Solutions for a Non-Newtonian Diffuse Interface Model with Different Densities" with D.Breit, Preprint arXiv:/1509.05663

Preprints, not submitted

  1. "Thermodynamically consistent diffuse interface models for incompressible two-phase flows with different densities" with H. Garcke and G. Grün, Preprint, arXiv:/1011.0528

Proceedings contributions

  1. "Reduced Stokes equations and bounded Hinfty-calculus", Proc. EquaDiff 2003, World Scientific, pp. 365-370, 2005.
  2. "Bounded imaginary powers and Hinfty-calculus of the Stokes operator in unbounded domains", Proceedings of the Conference Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann, Zürich, June 28-30, 2004. Progress in Nonlinear Diff. Eqns and their applications, Volume 64
  3. "The Stokes equations in asymptotically flat layers", Proceedings of the Conference ``Regularity and other Qualitative Aspects of the Navier-Stokes Equations'', Bedlewo, Poland, 2003, Banach Center Publications Volume 70, 9-19. 2005
  4. "On the notion of generalized solutions of viscous incompressible two-phase flows", Proceedings of the Kyoto Conference on ``Navier-Stokes equations and their Applications'', RIMS Kôkyûroku Bessatsu B1, 1-19, 2007.
  5. "Diffuse interface models for immiscible, viscous, incompressible fluids: modeling and mathematical properties", Proceedings of the ``International Conference on Multiphase Flows (ICMF 2007)'', Leipzig, 6 pages, 2007
  6. "Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system", Proceedings of the Conference ``Nonlocal and Abstract Parabolic Equations and their Applications'', Bedlewo, Poland, 2007, Banach Center Publ. Volume 86, 9-19, 2009
  7. "Double obstacle limit for a Navier-Stokes/Cahn-Hilliard system", inn ``Parabolic Problems. The Herbert Amann Festschrift'', Progress in Nonlinear Differential Equations and Their Applications, Vol. 60 , 1-20 in press.
  8. "Thin Vibrating Plates: Long Time Existence and Convergence to the von Karman Plate Equations" with M.G. Mora und S. Müller, GAMM-Mitt. 34, No. 1, 97 – 101 (2011) DOI 10.1002/gamm.201110015
  9. "Stationary Solutions for a Navier-Stokes/Cahn-Hilliard System with Singular Free Energies" with J. Weber, to appear in Proceedings of ICMFD in "Recent Developments of Mathematical Fluid Mechanics" Series: Advances in Mathematical Fluid Mechanics, Birhäueser-Verlag