In this talk, we consider a simplified model for radiating flows in $\mathbb{R}^3$. It consists of the compressible Navier-Stokes system with a $P1$-approximation of the transport equation. The global well-posedness of strong solutions in the Sobolev space $H^2(\mathbb{R}^3)$ for associated Cauchy problem is established when initial data are a small perturbation of a stable radiative equilibrium. Based on the energy method combined with the low-medium-high frequency decomposition, we develop a way to obtain the estimates of the solution and hence global existence. Furthermore, the optimal time decay rates of all-order spatial derivatives of the solutions are shown when the initial perturbation is additionally bounded in $L^1(\mathbb{R}^3)$.