On Shock Profiles in Four-Field Formulations of Dissipative Relativistic Fluid Dynamics

2023/03/21 by Heinrich Freistühler, Freistuhler, Heinrich · 2 citations
Environmental Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Methane Hydrates and Related Phenomena #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2303.11829

openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper shows that in second-order hyperbolic systems of partial differential equations proposed in authors' earlier paper (J. Math. Phys. 59 (2018)) for modelling the relativistic dynamics of barotropic fluids in the presence of viscosity and heat conduction, shock waves of arbitrary strength have smooth, monotone dissipation profiles. The results and arguments extend classical considerations of Weyl (Comm. Pure Appl. Math. 2 (1949)) and Gilbarg (Amer. J. Math. 73 (1951)) to the relativistic setting.

Cited by

• Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics
• Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods

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