Godunov variables and convex entropy for relativistic fluid dynamics with bulk viscosity

Abstract

Based on the conservation-dissipation formalism proposed by Zhu and collaborators we formulate a general version of the Israel-Stewart theory for relativistic fluid dynamics with bulk viscosity. Our generalization consists in allowing for a wide range of dependence of the entropy density on the bulk viscosity. We show the existence of Godunov-Boillat variables for this model. By known properties of systems possessing such variables, this provides an alternative proof of the recently established existence of solutions for the Israel-Stewart theory locally in time, and a proof that entropy production is positive across weak Lax shocks.

arXiv comment10 pages, v2: introduction modified, references added

References in corpus (4)

• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Nonlinear Constraints on Relativistic Fluids Far From Equilibrium
• Non-Linear Maximum Entropy Principle for a Polyatomic Gas subject to the Dynamic Pressure
• On the existence of solutions and causality for relativistic viscous conformal fluids