Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model

This paper concerns with the large time behavior of solutions to a diffusion approximation radiation hydrodynamics model when the initial data is a small perturbation around an equilibrium state. The global-in-time well-posedness of solutions is achieved in Sobolev spaces depending on the Littlewood-Paley decomposition technique together with certain elaborate energy estimates in frequency space. Moreover, the optimal decay rate of the solution is also yielded provided the initial data also satisfy an additional $L^1$ condition. Meanwhile, the similar results of the diffusion approximation system without the thermal conductivity could be also established.