A class of Hadamard well-posed five-field theories of dissipative relativistic fluid dynamics

Abstract

This paper proposes a class of causal formulations for dissipative relativistic fluid dynamics as a hyperbolic five-field system of second-order partial differential equations. The argumentation continues lines of thinking developed in the author’s earlier papers with Temple and generalizes a four-field description that was recently given by Bemfica, Disconzi, and Noronha [Phys. Rev. D 98, 104064 (2018)] for the case of the pure radiation fluid. The Navier–Stokes–Fourier-like models are constructed as perturbations of auxiliary “involutory augmentations” of the Euler equations and shown to be Hadamard well-posed at least at the level of their linearization.