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

TL;DR

This paper extends the Israel-Stewart theory for relativistic fluids with bulk viscosity by incorporating a broader entropy dependence, establishing Godunov variables, and proving local existence and positive entropy production.

Contribution

It generalizes the Israel-Stewart model using the conservation-dissipation formalism and demonstrates the existence of Godunov variables for this extended framework.

Findings

Existence of Godunov-Boillat variables for the generalized model

Proof of local-in-time solutions for the extended Israel-Stewart theory

Confirmation of positive entropy production across weak shocks

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.