Global Existence of Smooth Solutions for the Diffusion Approximation Model of General Gas in Radiation Hydrodynamics

Abstract

In this paper, we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics. The existence and uniqueness of global solutions is proved in perturbation framework, for more general gases including ideal polytropic gas. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density, velocity, temperature, and radiation field.