Decay rates of solutions to a P1-approximation model arising from radiation hydrodynamics

This paper is concerned with the global existence and large time behavior of solutions to Cauchy problem for a P1-approximation radiation hydrodynamics model. The global-in-time existence result is established in the small perturbation framework around a stable radiative equilibrium states in Sobolev space H4(R3). Moreover, when the initial perturbation is also bounded in L1(R3), the L2-decay rates of the solution and its derivatives are achieved accordingly. The proofs are based on the Littlewood-Paley decomposition techniques and elaborate energy estimates in different frequency regimes.