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Research interests

I am interested in the analysis and numerics of all kinds of partial differential equations arising in real world applications (with an emphasis on fluid dynamics).

  • Newtonian and generalized Newtonian fluid dynamics, incompressible turbulence
  • Fluid structure interaction
  • Fluidic interfaces, multiphase flow, phase transitions
  • Dynamics and equilibrium configurations of biological membranes
  • Nonlinear optics

Publications

Journal articles and preprints

  • "Asymptotic stability of local Helfrich minimizers", submitted.
  • "Local well-posedness for relaxational fluid vesicle dynamics" with Matthias Köhne, submitted.
  • "On a Stokes-type system arising in fluid vesicle dynamics", submitted.
  • "Functional setting for unsteady problems in moving domains and applications" with P. Nägele and M. Růžička, submitted.
  • "Weak solutions for an incompressible, generalized Newtonian fluid interacting with a linearly elastic Koiter type shell", SIAM J. Math. Anal. 46 (2014), no. 4, 2614-2649.
  • "On Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows" with H. Abels, Interfaces and Free Boundaries 16 (2014), no. 3, 395-418.
  • "Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell" with M. Růžička, Arch. Ration. Mech. Anal. 211 (2014), no. 1, 205-255.
  • "Partial regularity for minimizers of quasi-convex functionals with general growth" with L. Diening, B. Stroffolini, and A. Verde, SIAM J. Math. Anal. 44 (2012), no. 5, 3594-3616.
  • "Scalar conservation laws on constant and time-dependent Riemannian manifolds" with Th. Müller, J. Differential Equations 254 (2013), no. 4, 1705-1727.
  • "The Stokes and Poisson problem in variable exponent spaces" with L. Diening and M. Růžička, Complex Var. Elliptic Equ. 56 (2011), no. 7-9, 789-811.

Theses

  • "Regularitätstheorie in Räumen mit variablen Exponenten", Diploma thesis, University of Freiburg, 2008.
  • "Globale Existenz für die Interaktion eines Navier-Stokes-Fluids mit einer linear elastischen Schale", PhD thesis, University of Freiburg, 2011.

  1. Universität Regensburg