Scattering Limit of the Diffusion Approximate Model in Radiation Hydrodynamics

The multidimensional gray model in radiation hydrodynamics describing the energy and momentum exchanges between the fluid and the radiation field is considered. This exchange is accomplished by the absorption, scattering, and emission of photons. In the nonequilibrium frame, the scattering process is the dominated. Through the asymptotic expansion of the radiation intensity, an diffusion approximate model with small parameters is obtained from the gray one, which consists of compressible Euler equations and radiation diffusion equation. In this paper, we will discuss the scattering limit problem of the diffusion approximation model. We will show that when the scattering process tends to stop (i.e., the small parameter tends to zero), the smooth solution of the diffusion approximation model converges to the smooth solution of the so-called nonequilibrium model in radiation hydrodynamics. Both of these models are widely used in the study of radiation hydrodynamics.