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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, Book Chapters and Reviews

  1. Book review: Alain Miranville: “The Cahn–Hilliard Equation: Recent Advances and Applications”, Jahresbericht der Deutschen Mathematiker-Vereinigung,?123(1), 57-62, 2021; DOI 10.1365/s13291-020-00224-y
  2. "Pseudodifferential and Singular Integral Operators", Graduate Lecture, DeGruyter, 2011
  3. Chapter "Weak solutions and diffuse interface models for incompressible two-phase flows" ,with Harald Garcke, doi:10.1007/978-3-319-10151-4_29-1, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Springer; Preprint 2015 , pp 1-60, 2016

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", with Mathias Wilke, 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. R?ger, 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, Annali di Matematica Pura ed Applicata Vol. 194 pp 1071 - 1106, 2015; 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, 2014; 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. 95, No. 12, 1411–1427 (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, Vol. 15(4), pp. 913-959 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 Math. Nachr. Vol. 289, No. 2–3, pp. 136–174 (2016)/ DOI 10.1002/mana.201400102; 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, Adv. Diff. Eq. 21, No. 1-2, pp. 109-153, 2015; Preprint arXiv:1312.5988/.
  42. "Analysis of the diffuse domain approach for a bulk-surface coupled PDE system" with Kei Fong Lam, Bj?rn Stinner, SIAM J. Math. Anal., 47(5), 3687–3725; Preprint arXiv:1502.04902/.
  43. "Weak Solutions for a Non-Newtonian Diffuse Interface Model with Different Densities" with D.Breit, Preprint arXiv:/1509.05663, Nonlinearity Vol. 29, pp. 3426–3453, 2016
  44. "Spectral Invariance of Non-Smooth Pseudodifferential Operators" with Christine Pfeuffer, Preprint arxiv.org/abs/1512.08795, Integral Equations Operator Theory, Volume 86, Issue 1, pp 41–70, DOI 10.1007/s00020-016-2315-0
  45. "Characterization of Non-Smooth Pseudodifferential Operators" with
    Christine Pfeuffer, Journal of Fourier Analysis and Applications, "24(2), pp. 371-415" (2017). doi:10.1007/s00041-017-9529-7, Preprint arxiv.org/abs/1512.01127
  46. "Sharp Interface Limit for a Stokes/Allen-Cahn System" with Yuning Liu, Arch. Rational Mech. Anal. 229(1), pp. 417-502, 2018, DOI:10.1007/s00205-018-1220-x, Preprint http://arxiv.org/abs/1611.04422
  47. "Well-Posedness of a Navier-Stokes/Mean Curvature Flow system" with Maximilian Moser, Mathematical analysis in fluid mechanics—selected recent results, 1–23, Contemp. Math., 710, Amer. Math. Soc., Providence, RI, 2018. Preprint https://arxiv.org/abs/1705.10832
  48. ""Existence of Weak Solutions for a Diffuse Interface Model for
    Two-Phase Flow with Surfactants    " with Harald Garcke and Josef Weber, doi: 10.3934/cpaa.2019011, Communications on Pure and Applied Analysis 18(1), pp. 195-225, 2019, Preprint http://arxiv.org/abs/1710.03082
  49. "A Phase-Field Model for Fluid-Structure-Interaction" with Dominik Mokbel and Sebastian Aland, Journal of Computational Physics, Volume 372, pp. 823-840, 2018, https://doi.org/10.1016/j.jcp.2018.06.063, Preprint http://arxiv.org/abs/1803.02354
  50. "Standard Planar Double Bubbles are Stable under Surface Diffusion Flow" with N. Arab and H. Garcke,?Comm. Anal. Geom., Vol. 29, No. 5, 1007-1060, 2021, DOI:?https://dx.doi.org/10.4310/CAG.2021.v29.n5.a1; Preprint arXiv:/1505.02979 .
  51. "Nonsmooth Pseudodifferential Boundary Value Problems on Manifolds" with Carolina Neira Jiménez, Preprint http://arxiv.org/abs/1709.04157? Journal of Pseudo-Differential Operators and Applications, Volume 10, Issue 2, pp 415-453,http://link.springer.com/article/10.1007/s11868-018-0268-6, 2019
  52. "Pressure Reconstruction for Weak Solutions of the Two-Phase Incompressible Navier--Stokes Equations with Surface Tension" with Johannes Daube and Christiane Kraus, Preprint http://arxiv.org/abs/1801.04840 "Asymptotic Analysis" 113 (2019) 51–86
    DOI 10.3233/ASY-181507.
  53. "On a Model for Phase Separation on Biological Membranes and its Relation to the Ohta-Kawasaki Equation" with Johannes Kampmann, European J. Appl. Math. Vol. 31, Issue 2, pp. 297-338, 2020, DOI:http://dx.doi.org/10.1017/S0956792519000056, Preprint https://arxiv.org/abs/1810.06654.
  54. "Fredholm Property of Non-Smooth Pseudodifferential Operators" with Christine Pfeuffer, Math. Nachr., 2020;293:822–846 https://doi.org/10.1002/mana.201800361 , Preprint http://arxiv.org/abs/1806.01113.
  55. "Convergence of the Allen-Cahn Equation to the Mean Curvature Flow
    with $90^\circ$-Contact Angle in 2D" with Maximilian Moser, Interfaces Free Bound., Vol. 21, No. 3, pp. 313–365, 2019, DOI: 10.4171/IFB/425, Preprint http://arxiv.org/abs/1806.02065
  56. "Short Time Existence for the Curve Diffusion Flow with a Contact Angle"
    with Julia Butz, J. Diff. Eq. Vol. 268 Issue 1, pp. 318-352, 2019, DOI:
    https://doi.org/10.1016/j.jde.2019.08.018, preprint:
    https://arxiv.org/abs/1810.01502.
  57. "Existence of Weak Solutions for a Sharp Interface Model for Phase Separation on Biological Membranes" with Johannes Kampmann, Discrete Contin. Dyn. Syst. Ser. S. ; Vol. 14, No. 1, pp. 331-351, 2021; doi:?10.3934/dcdss.2020325
  58. "Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of
    Incompressible Fluids with Different Densities and Nonlocal Free Energies" with Yutaka Terasawa, Math Meth Appl Sci. Vol. 43, Issue 6, pp. 3200-3219, 2020 https://doi.org/10.1002/mma.6111; Preprint http://arxiv.org/abs/1806.01030
  59. "A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle" with Julia Butz, SIAM J. Math. Anal., Vol. 52, No. 3, pp. 2592-2623, 2020; DOI: 10.1137/19M1242914, Preprint http://arxiv.org/abs/1810.07257
  60. "Well-Posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact" with Maximilian Rauchecker and Mathias Wilke, Math. Ann. (2020) DOI: 10.1007/s00208-020-02007-3 , Preprint https://arxiv.org/abs/1902.03611
  61. "On a linearized Mullins-Sekerka/Stokes system for two-phase flows" with Andreas Marquardt, Discrete Contin. Dyn. Syst. Ser. S, 2020,