How to get in touch...
Helmut Abels
Faculty of mathematics
University of Regensburg
Universitätsstraße 31
D93053 Regensburg
Germany
Office: M 110
Phone: ++49 (0)941 943 4288
Fax: ++49 (0)941 943 3263
email: helmut.abels"at"mathematik.uniregensburg.de
Secratary: Karin Zirngibl, 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 W2professor (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 W2professor (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 NavierStokes 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 nonsmooth 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 TwoPhase Flows of Viscous, Incompressible Fluids"
Books
 "Pseudodifferential and Singular Integral Operators", Graduate Lecture, DeGruyter, 2011
Journal articles
 "L^{q}L^{r}estimates for nonstationary Stokes equations in an aperture domain", Z. Anal. Anwend. 21, No. 1, pp. 159178, 2002.

"Bounded imaginary powers of the Stokes operator in an infinite
layer", J. Evol. Eq. 2, pp. 439457, 2002

"Generalized Stokes resolvent equations in an infinite layer with
mixed boundary conditions", Math. Nachr. 279, No. 4, pp. 117, 2006

"Reduced and generalized Stokes resolvent equations in
asymptotically flat layers, part I: unique solvability",
J. Math. Fluid Mech. 7 No. 2, pp. 201222, 2005

"Reduced and generalized Stokes resolvent equations in
asymptotically flat layers, part II: H_{infty}calculus",
J. Math. Fluid Mech. 7 No. 2, pp. 223260, 2005

"The initial value problem for the NavierStokes equations with a free surface in L^{q}Sobolev spaces",
Adv. Diff. Eq. 10. No. 1, pp. 4564, 2005.

"Pseudodifferential boundary value problems with nonsmooth coeffficients",
Comm. Part. Diff. Eq. 30, pp. 14631503, 2005

"Bounded imaginary powers and H_{infty}calculus of the Stokes
operator in twodimensional exterior domains",
Math. Z. 251 No. 3, pp. 589605, 2005

"Resolvent estimates for the Stokes operator on an infinite layer" with M. Wiegner,
Diff. Int. Eq. 18 No. 10, pp. 10811110, 2005

"On generalized solutions of twophase flows for viscous incompressible fluids",
Interfaces Free Bound. 9 No. 1, pp. 3165, 2007

"An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control" with M. Kassmann,
J. Diff. Eq. 236 No. 1, pp. 2956, 2007
 "Convergence to equilibrium for the CahnHilliard equation with a logarithmic free energy", Nonlinear Anal. 67 No. 11, pp. 31763193, 2007

"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, 259276 ,2008

"On a diffuse interface model for a twophase flow of compressible viscous fluids" with E. Feireisl,
Indiana Univ. Math. J. 57 No. 2, pp. 659698, 2008

"On a diffuse interface model for twophase flows of viscous, incompressible fluids with matched densities", Arch. Rational Mech. Anal. 194, No. 2, 463506, 2009, DOI 10.1007/s0020500801602

"On hypoellipticity of generators of Levy processes" with R. Husseini, Ark. Mat. 48 No. 2, 2010, pp. 231242 DOI 10.1007/s0020500801602

"On Stokes operators with variable viscosity in bounded and unbounded domains" with Y. Terasawa, Math. Ann. 344, No. 2, pp. 381429 , 2009 DOI 10.1007/s0020800803117

"The Cauchy problem and the martingale problem for integrodifferential operators with nonsmooth kernels" with M. Kassmann, Osaka J. Math. 46, pp. 123, 2009

"Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities", Comm. Math. Phys. Vol. 289, No. 1, pp. 4573, 2009

"Existence of weak solutions for a
nonclassical sharp interface model for a twophase flow of viscous,
incompressible fluids" with M. Röger, Annales de l'Institut Henri Poincare (C) Non Linear Analysis Vol. 26, pp. 24032424, 2009, DOI 10.1016/j.anihpc.2009.06.002

"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. 141157, 2010, doi:10.3934/dcdss.2010.3.141

"Nonhomogeneous NavierStokes systems with orderparameter dependent stresses" with Y. Terasawa, Math. Methods Appl. Sci., Vol. 33., No. 13, pp. 15321544, 2010

"The timedependent von Kármán plate equation as a limit of 3d nonlinear elasticity" with M.G. Mora and S. Müller, Calc. Var., Vol. 41, No. 12, pp. 241259, 2011 DOI: 10.1007/s0052601003600

"Thermodynamically consistent, frame indifferent diffuse interface models for incompressible twophase 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,

"Large time existence for thin vibrating plates" with M.G. Mora and S. Müller, Comm. Partial Differential Equations 36, pp. 20622102, 2011

"Strong WellPosedness of a Diffuse Interface Model for a Viscous, QuasiIncompressible TwoPhase Flow", SIAM J. Math. Anal. 44, No.1, pp. 316340, 2012; DOI: 10.1137/110829246, Preprint.

"Existence of Weak Solutions for a Diffuse Interface Model for TwoPhase Flows of
Incompressible Fluids with Different Densities" with D. Depner and H. Garcke, J. Math. Fluid Mech., Vol. 15, No. 3, pp. 453480, 2013, Preprint arXiv:/1111.2493

"WellPosedness and Qualitative Behaviour of Solutions for a TwoPhase NavierStokesMullinsSekerka System" with M. Wilke, Interfaces Free Bound., Vol. 15, No. 1, pp. 39–75, 2013
DOI: 10.4171/IFB/294; Preprint, arXiv:/1201.0179.

"On an incompressible NavierStokes/CahnHilliard 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. 11751190, 2013
; Preprint, arXiv:/1210.1011.

"Existence of Weak Solutions for a Diffuse Interface Model of NonNewtonian TwoPhase Flows" with L. Diening and Y. Terasawa, Nonlinear Analysis Series B: Real World Applications, Vol. 15, pp. 149–157, 2014; Preprint: arXiv:/1302.3107.

"Extension theory and Kreintype 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

"CahnHilliard 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/.

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/.

"On Sharp Interface Limits for Diffuse Interface Models for TwoPhase Flows" with D. Lengeler, Interfaces Free Bound. Vol. 16, No. 3, pp. 395–418, 2014 ; Preprint, arXiv:/1212.5582.

"Wellposedness of a fullycoupled NavierStokes/Qtensor 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/.
 "Sharp Interface Limit for the CahnLarche System" with S. Schaubeck, Asymptotic Analysis, Vol. 91, pp. 283–340, 2015;
preprint: arXiv:1403.1151/
 "Classical Solutions for a Modified HeleShaw Model with Elasticity" with S. Schaubeck, Z. Angew. Math. Mech., pp. 1–17, 2015.
 "Stability of Spherical Caps under the VolumePreserving Mean Curvature Flow with Line Tension" with H. Garcke and L. Müller, Nonlinear Analysis, Vol. 117, pp. 8–37, 2015; preprint arXiv:/1403.1139
 "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/s0002801502871; Preprint arXiv:/1403.4526
 "Local WellPosedness for VolumePreserving Mean Curvature and Willmore Flows with Line Tension" with H. Garcke and L. Müller to appear in Math. Nachr.; Preprint arXiv:1403.1132/

"Strong solutions for the BerisEdwards 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/.

"Analysis of the diffuse domain approach for a bulksurface coupled PDE
system" with Kei Fong Lam, Björn Stinner, accepted for publication in SIAM J. Math. Anal.; Preprint arXiv:1502.04902/.
Preprints, submitted
 "Standard Planar Double Bubbles are Stable under Surface Diffusion Flow" with N. Arab and H. Garcke, Preprint arXiv:/1505.02979
 "Weak Solutions for a NonNewtonian Diffuse Interface Model with Different Densities" with D.Breit, Preprint arXiv:/1509.05663
Preprints, not submitted

"Thermodynamically consistent diffuse interface models for incompressible twophase flows with different densities" with H. Garcke and G. Grün, Preprint, arXiv:/1011.0528
Proceedings contributions

"Reduced Stokes equations and bounded H_{infty}calculus",
Proc. EquaDiff 2003, World Scientific, pp. 365370, 2005.

"Bounded imaginary powers and H_{infty}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 2830, 2004. Progress in Nonlinear Diff. Eqns and their applications, Volume 64

"The Stokes equations in asymptotically flat layers",
Proceedings of the Conference ``Regularity and other Qualitative Aspects of the NavierStokes Equations'', Bedlewo, Poland, 2003, Banach Center Publications Volume 70, 919. 2005

"On the notion of generalized solutions of viscous incompressible twophase flows", Proceedings of the Kyoto Conference on ``NavierStokes equations and their Applications'', RIMS Kôkyûroku Bessatsu B1, 119, 2007.

"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

"Longtime behavior of solutions of a NavierStokes/CahnHilliard
system",
Proceedings of the Conference ``Nonlocal and Abstract Parabolic
Equations and their Applications'', Bedlewo, Poland, 2007, Banach Center Publ. Volume 86, 919, 2009

"Double obstacle limit for a NavierStokes/CahnHilliard system",
inn ``Parabolic Problems. The Herbert Amann Festschrift'', Progress in Nonlinear Differential Equations
and Their Applications, Vol. 60 , 120 in press.
 "Thin Vibrating Plates: Long Time Existence and Convergence to the von Karman Plate Equations" with M.G. Mora und S. Müller, GAMMMitt. 34, No. 1, 97 – 101 (2011) DOI 10.1002/gamm.201110015
 "Stationary Solutions for a NavierStokes/CahnHilliard 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, BirhäueserVerlag
