On a simplified model for radiating flows

Abstract

We consider a simplified model arising in radiation hydrodynamics which is based on the barotropic Navier–Stokes system describing the macroscopic fluid motion and a P1-approximation (see below) of the transport equation modeling the propagation of radiative intensity. We establish global-in-time existence of strong solutions for the associated Cauchy problem when initial data are close to a stable radiative equilibrium and local existence for large data with no vacuum. All our results are stated in the so-called critical Besov spaces.