The combined non-equilibrium diffusion and low Mach number limits of the compressible Navier-Stokes-Fourier-P1 approximation radiation model

Abstract

In this paper, we investigate the combined non-equilibrium diffusion and low Mach number limits of the compressible Navier-Stokes-Fourier-P1 (NSF-P1) model with general initial data, which arises in the radiation hydrodynamics. Compared to the classical compressible Navier-Stokes-Fourier system, the NSF-P1 model has an asymmetric singular structure caused by the radiation field. To handle these singular terms, we introduce an equivalent pressure and an equivalent velocity to balance the order of singularity and establish the uniform estimates of solutions by designating appropriate weighted norms as well as carrying out delicate energy analysis. We conclude that, for partially general initial data and the strong scattering effect, the NSF-P1 model converges to the system of low Mach number heat-conducting viscous flows coupled with a diffusion equation. We also discuss the variations of the limit equations as the scattering intensity changes. Furthermore, when the scattering effect is sufficiently weak, we can obtain the singular limits of the NSF-P1 model with fully general initial data.