Partial differential equations in mathematical fluid mechanics
Convex integration, admissibilty criteria, existence and (non-)uniqueness of solutions
Relativistic fluid dynamics
Singular perturbations of dynamical systems
Publications
Articles in Peer-Reviewed Journals
VP: Relativistic shock profiles as an instance of two-scale spatial dynamics. Phys. D: Nonlinear Phenom. 453, 133856 (2023).
Link
VP: A generically singular type of saddle-node bifurcation that occurs for relativistic shock waves. Phys. D: Nonlinear Phenom. 453, 133829 (2023).
Link
H. Freistühler , VP: Dependence on the background viscosity of solutions to a prototypical non-strictly hyperbolic system of conservation laws. SIAM J. Math. Anal., 52(6), 5658-5674 (2020).
Link
Articles in Peer-Reviewed Conference Proceedings
VP: Oscillating Shock Profiles in Relativistic Fluid Dynamics. In Pares C., Castro, M.J., Morales de Luna, T., Munoz-Ruiz, M.L. (eds)
Hyperbolic Problems: Theory, Numerics, Applications. Volume I. HYP 2022. SEMA SIMAI Springer Series, vol 34. Springer, Cham. (2024) Link
Preprints
S. Markfelder , VP: Failure of the least action admissibility principle in the context of the compressible Euler equations, 2025. arXiv: 2502.09292. Link
Poster
Shock Profiles in Dissipative Relativistic Fluid Dynamics, Poster presented at SPP2410 Workshop: Analysis of Dissipation in Inviscid and Compressible Fluid Dynamics, 2024, Link.
Dependence on the Background Viscosity of
Solutions to Non-Strictly Hyperbolic Systems,
with Applications to Magnetohydrodynamics, Poster presented at numhyp23 : Numerical Methods for Hyperbolic Problems, 2023, Link.
