Existence of strong solutions with critical regularity to a polytropic model for radiating flows

This paper is the continuation of our recent work Danchin and Ducomet (J Evol Equ 14:155-195, 2013) devoted to barotropic radiating flows. We here aim at investigating the more physically relevant situation of polytropic flows. More precisely, we consider a model arising in radiation hydrodynamics which is based on the full Navier-Stokes-Fourier system describing the macroscopic fluid motion, and a P1-approximation (see below) of the transport equation modeling the propagation of radiative intensity. In the strongly under-relativistic situation, we establish the global-in-time existence and uniqueness of solutions with critical regularity for the associated Cauchy problem with initial data close to a stable radiative equilibrium. We also justify the nonrelativistic limit in that context. For smoother (possibly) large data bounded away from the vacuum and more general physical coefficients that may depend on both the density and the temperature, the local existence of strong solutions is shown.