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Veröffentlichungsliste/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"


  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