Global Well-Posedness and Large-Time Behavior for the Equilibrium Diffusion Model in Radiation Hydrodynamics

In this paper, we investigate the global well-posedness of the equilibrium diffusion model in radiation hydrodynamics. The model consists of the compressible Navier-Stokes equations coupled with radiation effect terms described by the fourth power of temperature. The global existence of classical solutions to the Cauchy problem in the whole space is established when initial data is a small smooth perturbation of a constant equilibrium state: moreover, an algebraic rate of convergence of solutions toward equilibrium is obtained under additional conditions on initial data. The proof is based on the refined energy method and Fourier’s analysis.