Nonrelativistic Limit of the Compressible Navier--Stokes--Fourier--P1 Approximation Model Arising in Radiation Hydrodynamics

It is well known that the general radiation hydrodynamics models include two mainly coupled parts: one is the macroscopic fluid part, which is governed by the compressible Navier--Stokes--Fourier equations; another is the radiation field part, which is described by the transport equation of photons. Under the two physical approximations, gray approximation and P1 approximation, one can derive the so-called Navier--Stokes--Fourier--P1 approximation radiation hydrodynamics model from the general one. In this paper, we study the nonrelativistic limit problem for the Navier--Stokes--Fourier--P1 approximation model due to the fact that the speed of light is much larger than the speed of the macroscopic fluid. Our results give a rigorous derivation of the widely used macroscopic model in radiation hydrodynamics.