Global existence and optimal time-decay rates of 3D non-isentropic compressible Navier-Stokes system with potential force

This paper concerns the global existence and optimal time-decay rate for the higher-order spatial derivative of classical solutions for the three-dimensional viscous and heat-conductive fluids, which is governed by the compressible Navier-Stokes (CNS) system with an external potential force. We first establish the global existence of the non-isentropic CNS system with potential force when the initial data is a small perturbation near the equilibrium state. Subsequently, we show the upper and lower bounds of the optimal decay rates for the solution and its spatial derivatives based on energy estimate and low-high frequency decomposition.