How to get in touch...
Faculty of mathematics
University of Regensburg
Office: M 110
Phone: ++49 (0)941 943 4288
Fax: ++49 (0)941 943 3263
Secratary: Karin Zirngibl, Office M 218, Tel. ++49 (0) 941 943 2390
| 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
- 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
- Lecture notes to the course on pseudodifferential operators, autumn term 2003/04, TU Darmstadt: PsDOSkript.ps
List of publications
"Stokes Equations in Asymptotically Flat Domains and the Motion
of a Free Surface", Dissertation, TU Darmstadt, Shaker Verlag, Aachen, 2003.
"Diffuse Interface Models for Two-Phase Flows of Viscous, Incompressible Fluids"
- "Pseudodifferential and Singular Integral Operators", Graduate Lecture, DeGruyter, 2011
- "Lq-Lr-estimates for non-stationary Stokes equations in an aperture domain", Z. Anal. Anwend. 21, No. 1, pp. 159-178, 2002.
"Bounded imaginary powers of the Stokes operator in an infinite
layer", J. Evol. Eq. 2, pp. 439-457, 2002
"Generalized Stokes resolvent equations in an infinite layer with
mixed boundary conditions", Math. Nachr. 279, No. 4, pp. 1-17, 2006
"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
"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
"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.
"Pseudodifferential boundary value problems with non-smooth coeffficients",
Comm. Part. Diff. Eq. 30, pp. 1463-1503, 2005
"Bounded imaginary powers and Hinfty-calculus of the Stokes
operator in two-dimensional exterior domains",
Math. Z. 251 No. 3, pp. 589-605, 2005
"Resolvent estimates for the Stokes operator on an infinite layer" with M. Wiegner,
Diff. Int. Eq. 18 No. 10, pp. 1081-1110, 2005
"On generalized solutions of two-phase flows for viscous incompressible fluids",
Interfaces Free Bound. 9 No. 1, pp. 31-65, 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. 29-56, 2007
- "Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy", Nonlinear Anal. 67 No. 11, pp. 3176-3193, 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, 259-276 ,2008
"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
"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
"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
"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
"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
"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
"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
"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
"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
"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
"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,
"Large time existence for thin vibrating plates" with M.G. Mora and S. Müller, Comm. Partial Differential Equations 36, pp. 2062-2102, 2011
"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.
"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
"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.
"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.
"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.
"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
"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/.
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 Two-Phase Flows" with D. Lengeler, Interfaces Free Bound. Vol. 16, No. 3, pp. 395–-418, 2014 ; Preprint, arXiv:/1212.5582.
"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/.
- "Sharp Interface Limit for the Cahn-Larche System" with S. Schaubeck, Asymptotic Analysis, Vol. 91, pp. 283-–340, 2015;
- "Classical Solutions for a Modified Hele-Shaw Model with Elasticity" with S. Schaubeck, Z. Angew. Math. Mech., pp. 1–-17, 2015.
- "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
- "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
- "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/
"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/.
"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/.
- "Standard Planar Double Bubbles are Stable under Surface Diffusion Flow" with N. Arab and H. Garcke, Preprint arXiv:/1505.02979
- "Weak Solutions for a Non-Newtonian Diffuse Interface Model with Different Densities" with D.Breit, Preprint arXiv:/1509.05663
Preprints, not submitted
"Thermodynamically consistent diffuse interface models for incompressible two-phase flows with different densities" with H. Garcke and G. Grün, Preprint, arXiv:/1011.0528
"Reduced Stokes equations and bounded Hinfty-calculus",
Proc. EquaDiff 2003, World Scientific, pp. 365-370, 2005.
"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
"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
"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.
"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 Navier-Stokes/Cahn-Hilliard
Proceedings of the Conference ``Nonlocal and Abstract Parabolic
Equations and their Applications'', Bedlewo, Poland, 2007, Banach Center Publ. Volume 86, 9-19, 2009
"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.
- "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
- "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