Equilibrium and Non‐Equilibrium Diffusion Limits for the Compressible Navier–Stokes–Fourier‐P1 Approximation Model of Radiative Flow

In this paper, we study both equilibrium and non‐equilibrium diffusion limits of the compressible Navier–Stokes–Fourier‐P1 approximation model arising in radiation hydrodynamics. In the Sobolev functional framework, we establish the uniform estimates of strong solutions with respect to the transport coefficients and prove the convergence to the limiting systems. In the non‐equilibrium regime, the limiting system consists of a compressible Navier–Stokes–Fourier system coupled with a diffusion equation, while the radiative equilibrium is achieved between matter and radiation with the leading term of radiation distribution in the equilibrium regime.