Non-Existence and Existence of Shock Profiles in the Bemfica-Disconzi-Noronha Model

TL;DR

This paper investigates shock wave profiles in a hyperbolic PDE model for viscous radiation fluids, revealing a dichotomy where small shocks have profiles but larger ones may not, depending on model parameters.

Contribution

It establishes the existence and non-existence of shock profiles in the Bemfica-Disconzi-Noronha model based on parameter choices, highlighting a novel dichotomy.

Findings

Small amplitude shocks admit profiles.

Certain large shocks do not admit profiles.

The existence of profiles depends on the model's parameters.

Abstract

This note studies a four-field hyperbolic PDE model that was recently introduced by Bemfica, Disconzi, and Noronha for the pure radiation fluid with viscosity, and asks whether shock waves admit continuous profiles in this description. The model containing two free parameters mu, nu and being causal whenever one chooses (mu,nu) from a certain range C subset R2, this paper shows that for any choice of (mu,nu) in the interior of C, there is a dichotomy in so far as (i) shocks of sufficiently small amplitude admit profiles and (ii) certain other, thus necessarily non-small, shocks do not. This finding does not preclude the possibility that if one chooses (mu,nu) from a specific part S of the boundary of C, the dichotomy disappears and all shocks have profiles; the parameter set S corresponds to the "sharply causal" case, in which one of the characteristic speeds of the dissipation operator is the speed of light.