The Low Mach Number Limit for a Barotropic Model of Radiative Flow

We aim at justifying rigorously the low Mach number asymptotics for a model of compressible fluid coupled to the radiation. For simplicity, we restrict ourselves to the barotropic situation, and adopt the so-called P1-approximation to model the effects of radiation. We focus on small perturbations of stable constant equilibria. In the critical regularity framework, we establish estimates independent of the Mach number, and convergence results to the incompressible Navier-Stokes equation, exactly as in the non radiative case. Our results hold true in the whole space R as well as in a periodic box T with n ≥ 2.