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

This paper concerns 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 rates of solutions are also derived provided the initial data satisfy an additional L 1 condition. Meanwhile, the same decay rates of the solutions to the approximation system without thermal conductivity could also be established.