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 H 4 ( R 3 ) . Moreover, when the initial perturbation is also bounded in L 1 ( R 3 ) , the L 2 -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.