报告摘要：
| This paper is concerned with the global existence and large time behavior of solutions to Cauchy problem for a P1-approximation radiation hydrodynamics model as well as the pointwise estimates about the solution for approximation radiation hydrodynamic model with damping. The global-in-time existence result is established in the small perturbation framework around a stable radiative equilibrium states in Sobolev space $H^4(mathbb{R}^3)$. Moreover, when the initial perturbation is also bounded in $L^1(mathbb{R}^3)$, 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. On the ohter hand, the pointwise estimates of the solution is established by the precise estimates on the Green function of the linear system. This is a jointed work with Shijin Deng, Wenjun Wang and Feng Xie.
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