Nonexistence and existence of shock profiles in the Bemfica-Disconzi-Noronha model

This paper 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 of R-2, 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 nonsmall, 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.

Automated summary

This paper studies a four-field hyperbolic PDE model for the pure radiation fluid with viscosity, and shows that there is a dichotomy in the profiles of shock waves for certain choices of parameters. It is found that for specific boundary conditions, all shock waves may have profiles, indicating a different behavior compared to the interior choices of parameters.