Long-time behavior for three dimensional compressible viscous and heat-conductive gases

We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conductive gases in $\mathbb{R}^3$. More precisely, under a suitable additional condition involving only the low frequencies of the initial data, we exhibit the optimal time decay rates for the constructed global solutions. The proof relies on some new energy arguments developed by Xin and Xu [39] for the compressible Navier-Stokes equations.