In this talk, I will present some new studies on approximation radiation hydrodynamic system, which arises from the macroscopic fluid motion of the radiation hyperbolic system. Firstly, I will recall the existence and the pointwise estimates of the solution of the radiation hydrodynamic system. Secondly, the asymptotic stability of the rarefaction waves of the radiation hydrodynamic limit model. I will focus on the difference between the radiation hydrodynamic system and the compressible Navier-Stokes equations and point out the radiation effect on the studies.