How to get in touch...

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 2576
e-mail: helmut.abels"at"mathematik.uni-regensburg.de
Secratary: Karin Zirngbl, Office M 218, Tel. ++49 (0) 941 943 2390

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"

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., 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", Preprint, Max Planck Institut for Mathematics in the Sciences, No. 12/2009, accepted for publication in Discrete Contin. Dyn. Syst. Ser. S (Special volume in honour of V.A. Solonnikov).
  22. "Non-homogeneous Navier-Stokes systems with order-parameter dependent stresses" with Y. Terasawa, Preprint, Max Planck Institut for Mathematics in the Sciences, No. 19/2009, to appear in Math. Methods Appl. Sci.

Preprints

  1. "Large time existence for thin vibrating plates" with M.G. Mora and S. Müller, Preprint, NWF I - Mathematik, Universität Regensburg, No. 20/2009, submitted
  2. "The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity" with M.G. Mora and S. Müller, Preprint, arXiv:0912.4135, 2009, submitted

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