Global existence and optimal decay rate of the classical solution to 3-D radiative hydrodynamics model with or without heat conductivity

Abstract

The classical solution of the 3-D radiative hydrodynamics model is studied in Hk-norm under two different conditions, with and without heat conductivity. We have proved the following results in both cases. First, when the Hk norm of the initial perturbation around a constant state is sufficiently small and the integer k≥2, a unique classical solution to such Cauchy problem is shown to exist. Second, if we further assume that the L1 norm of the initial perturbation is small too, the i-order (0≤i≤k−2) derivatives of the solutions have the decay rate of (1+t)−34−i2 in H2 norm. Third, from the results above we can see that for radiative hydrodynamics, the radiation can do the same job as that the heat conduction does, which means if the thermal conductivity coefficient turns to 0, because of the effect of radiation, the solvability of the system and decay rate of the solutions stay the same.