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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, doi: 10.3934/dcdss.2020467; Preprint https://arxiv.org/abs/2006.01654

  62. "On the Sharp Interface Limit of a Model for Phase Separation on Biological Membranes" with Johannes Kampmann, Analysis vol. 41, no. 1, 2021, pp. 37-60, DOI:10.1515/anly-2019-0019, Preprint https://arxiv.org/abs/1811.12489

  63. "Local Well-Posedness of a Quasi-Incomressible Two-Phase Flow." with Josef Weber, Journal Evol. Equ., vol. 21, pp. 3477-3502, 2021, https://doi.org/10.1007/s00028-020-00646-2 Preprint: https://arxiv.org/abs/2006.14251

  64. "Well posedness of the Muskat problem in subcritical Lp-Sobolev spaces" with Bogdan-Vasile Matioc, European J. of Appl. Math., vol. 33, no. 2, pp.224-266, 2022; DOI:10.1017/S0956792520000480, Preprint https://arxiv.org/abs/2003.07656

  65. "Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part II:
    Approximate Solutions" with Andreas Marquardt,?"J. Math. Fluid Mech. Vol. 23, Article number: 38, (2021), doi: https://doi.org/10.1007/s00021-021-00565-3;" , Preprint http://arxiv.org/abs/2003.14267

  66. "Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part I: Convergence Result" with Andreas Marquardt,? Interfaces Free Bound. pp. 353-402, Vol. 23, 2021; DOI 10.4171/IFB/457 Preprint http://arxiv.org/abs/2003.03139.

  67. "Invariance of the Fredholm Index and Spectrum of Non-Smooth
    Pseudodifferential Operators" with Christine Pfeuffer, Analysis and Applications, vol.20, no. 3, pp. 429-464, 2022, doi.org/10.1142/S0219530521500111, Preprint http://arxiv.org/abs/2003.00966

  68. "Convergence of the Allen-Cahn equation with a nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle close to 90°", with Maximilian Moser, SIAMJ. Math. Anal., vol. 54, no.1, pp. 114–172, 2022. Preprint http://arxiv.org/abs/2105.08434

  69. "(Non-)Convergence of Solutions of the Convective Allen-Cahn Equation", Helmut Abels, Partial Differ. Equ. Appl., vol. 3, no. 1, Paper No. 1, 11 pp, 2022. https://doi.org/10.1007/s42985-021-00140-5; Preprint https://arxiv.org/abs/2102.10057.

  70. "Large Times Existence for Thin Vibrating Rods" with Tobias Ameismeier, Asymptotic Analysis vol. 131, No. 3-4, pp. 471–512, 2023, DOI10.3233/ASY-221778 , Preprint http://arxiv.org/abs/2109.11618

  71. "Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities" with Yutaka Terasawa, Preprint: http://arxiv.org/abs/2201.06101 , Discrete Contin. Dyn. Syst. Ser. S vol. 15, no.8, pp. 1871-1881, 2022.

  72. "Convergence of Thin Vibrating Rods to a Linear Beam Equation" with Tobias Ameismeier, "Z. Angew. Math. Phys. 73, article no.166, 2022. https://doi.org/10.1007/s00033-022-01803-y", Preprint http://arxiv.org/abs/2110.01064

  73. "On a fluid-structure interaction problem for plaque growth" with Yadong Liu, Nonlinearity, Vol. 36, No. 1, pp. 537-583, 2023; doi: https://doi.org/10.1088/1361-6544/aca5e1, Preprint https://arxiv.org/abs/2110.00042??

  74. "On a fluid-structure interaction problem for plaque growth: cylindrical domain" with Yadong Liu, Journal of Differential Equations, vol. 345, pp. 334–400, 2023,doi: https://doi.org/10.1016/j.jde.2022.11.046; Preprint https://arxiv.org/abs/2112.12538 .

  75. "Fractional-Order Operators on Nonsmooth Domains" with Gerd Grubb, Preprint http://arxiv.org/abs/2004.10134 , published online in J. LondonMath. Soc., DOI:10.1112/jlms.12712.

  76. "Short Time Existence for Coupling of Scaled Mean Curvature Flow and Diffusion" with Felicitas Bürger and Harald Garcke, ?J. Evol. Equ., vol. 23, article no. 14, 46 pp.,? 2023, https://doi.org/10.1007/s00028-022-00861-z. Preprint https://arxiv.org/abs/2204.07626

  77. "Qualitative Properties for a System Coupling Scaled Mean Curvature Flow and Diffusion" with Felicitas Bürger and Harald Garcke, ?J. Differential Equations, vol. 345,pp. 334–400, 2023, https://doi.org/10.1016/j.jde.2022.11.046 Preprint https://arxiv.org/abs/2205.02493

  78. "Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System with Different Viscosities" with Mingwen Fei, SIAM J. Math. Anal., Vol. 55, No. 4, pp. 4039-4088, 2023, doi:10.1137/22M1523698, Preprint: http://arxiv.org/abs/2201.09343

  79. "Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities" with Harald Garcke and Andrea Giorgini, Math. Ann. 389, 1267–1321 (2024). https://doi.org/10.1007/s00208-023-02670-2; Preprint http://arxiv.org/abs/2209.10836??

  80. "Short time existence of a quasi-stationary fluid-structure interaction problem for plaque growth" with Yadong Liu, Advances in Nonlinear Analysis, vol. 12, no. 1, 2023, pp.20230101. https://doi.org/10.1515/anona-2023-0101; preprint: https://arxiv.org/abs/2208.06280.

  81. "Sharp Interface Limit for a Navier-Stokes/Allen-CahnSystem in the Case of a Vanishing Mobility" with Mingwen Fei and Maximilian Moser,?Calc. Var. 63, 94 (2024). https://doi.org/10.1007/s00526-024-02715-7, Preprint: https://arxiv.org/abs/2304.12096

  82. "Mathematical Analysis of a Diffuse Interface Modelfor Multi-Phase Flows? of Incompressible Viscous Fluids with Different Densities" with Harald Garcke and Andrea Poiatti, J. Math. Fluid Mech. (2024) 26:29; https://doi.org/10.1007/s00021-024-00864-5, Preprint: https://arxiv.org/abs/2308.11813

  83. "Strong Nonlocal-to-Local Convergence of the Cahn-Hilliard Equation and its Operator" with Christoph Hurm, Journal of Differential Equations 402, 593–624 (2024), Preprint: https://arxiv.org/abs/2307.02264

  84. "Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier-Stokes/Allen-Cahn System" with Julian Fischer and Maximilian Moser, Arch Rational Mech Anal 248, 77 (2024) https://doi.org/10.1007/s00205-024-02020-9, Preprint: http://arxiv.org/abs/2311.02997

  85. "Low Mach Number Limit of a Diffuse Interface Model for Two-Phase Flows of Compressible Viscous Fluids" with Yadong Liu and ?árka Ne?asová, GAMM-Mitteilungen. (2024), Preprint: https://arxiv.org/abs/2402.04372

  86. "Existence of Weak Solutions to a Cahn-Hilliard-Biot System" with Jonas Haselb?ck and Harald Garcke,? Nonlinear Anal. RWA 81 (2025) 104194; Preprint: arXiv:2403.07515

  87. "Mixture theory for diffuse interface models of two-phase flows", J. Fluid Mech. (2024), vol. 992, F1, doi:10.1017/jfm.2024.638

  88. "Maximal Lp-regularity for x-dependent fractional heat equations with Dirichlet conditions" with Gerd Grubb,?Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02999; Preprint: https://arxiv.org/abs/2312.01864

  89. "Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with? Different Densities: Global Well-Posedness" with Harald Garcke and Andrea Poiatti, Preprint: https://arxiv.org/abs/2408.07449?accepted for publication in Calc. Var. Part. Diff. Eq.

  90. "Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness" with Harald Garcke and Andrea Poiatti,?Calc. Var. 64, 141 (2025). https://doi.org/10.1007/s00526-025-03001-w, Preprint: https://arxiv.org/abs/2407.14941

?Preprints, submitted

  1. "Convergence of the Nonlocal Allen-Cahn Equationto Mean Curvature Flow" with Christoph Hurm and Maximilian Moser, Preprint: https://arxiv.org/abs/2410.08596

  2. "On a diffuse interface model for diblock copolymers interacting with an electric field" with Andrea di Primio and Harald Garcke, Preprint:?https://arxiv.org/abs/2411.04074

  3. "Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions" with Harald Garcke and Julia Wittmann, Preprint:?https://arxiv.org/abs/2505.05383

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 K?ky?roku 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", in "Parabolic Problems. The Herbert Amann Festschrift'', Progress in Nonlinear Differential Equations and Their Applications, Vol. 80 , 1-20 Birkh?user/Springer Basel AG, Basel, 2011.
  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, Proceedings of ICMFD in "Recent
    Developments of Mathematical Fluid Mechanics" Series: Advances in
    Mathematical Fluid Mechanics, pp. 25-41, Birkh?user-Verlag, 2016. And
    "Existance of Weak Solutions for a Diffuse Interface Model of Power-Law Type Two-Phase Flows" with Y. Terasawa, and Lars Diening, Proceedings of ICMFD in "Recent Developments of Mathematical Fluid Mechanics" Series: Advances in Mathematical Fluid Mechanics, pp. 13 - 23, Birkh?user-Verlag, 2016.
  10. "Nonconvergence of the Capillary Stress Functional for Solutions of the
    Convective Cahn-Hilliard Equation    " with S. Schaubeck, in "Proceedings of International Conference on Mathematical Fluid Dynamics, Present and Future", pp. 3-23, Springer Proceedings in Mathematics and Statistics 2016
  11. "Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities" with Harald Garcke, Günther Grün and Stefan Metzger in "Transport Processes at Fluidic Interfaces". Series: Advances in Mathematical Fluid Mechanics, pp 203 - 229, Birkh?user Verlag 2017
  12. "Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids" with Yuning Liu and Andreas Sch?ttl in "Transport Processes at Fluidic Interfaces". Series: Advances in Mathematical Fluid Mechanics, pp 231 - 253, Birkh?user Verlag 2017
  13. "Two-Phase Flow with Surfactants: Diffuse Interface Models and Their Analysis" with Harald Garcke, Kei Fong Lam and Josef Weber in "Transport Processes at Fluidic Interfaces". Series: Advances in Mathematical Fluid Mechanics, pp 255 - 270, Birkh?user Verlag 2017
  14. "The Sharp-Interface Limit of the Navier-Stokes-Korteweg Equations" with Johannes Daube, Christiane Kraus und Dietmar Kr?ner, in "Theory, Numerics and Applications of Hyperbolic Problems I", pp. 1-13, Springer Proceedings in Mathematics and Statistics 2018

Saskia Lindenberg - 13.05.2025 11:21

  1. HOMEPAGE UR

Faculty of Mathematics

 

Prof. Dr. Helmut Abels

Samm2015 Abels

Contact:
Building M, Room 110
Phone: 0941/943-4288
Assistant:
Saskia Lindenberg
Building M, Room 218
Phone: 0941/943-2390