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

Abstract

Based on the conservation–dissipation formalism proposed by Zhu et al. [J. Non-Equilib. Thermodyn. 40, 67 (2015)], 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.