In this talk, we consider the non-isentropic compressible Navier–Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. This equation models a compressible viscous, heat-conductive, and Newtonian polytropic fluid. We show the unique existence of stationary solutions for the perturbed half-space. The stationary solution depends on all directions and has multidirectional flow. We also prove the asymptotic stability of this stationary solution. This talk is based on joint work with Prof. Mingjie Li (Minzu University of China) and Prof. Katherine Zhiyuan Zhang (Northeastern University).