Large-time behavior for compressible Navier–Stokes equations subject to large external potential forces in a three-dimensional bounded domain

This paper investigates the large-time behavior for compressible Navier–Stokes equations subject to large external potential forces in a three-dimensional (3D) bounded domain with slip boundary conditions. Under the assumptions of small initial energy and a positive lower bound on the initial density, we prove that the density decays exponentially to the steady-state in the $L^{\infty }$-norm. Moreover, we show that vacuum states persist when the initial density contains vacuum (even at a single point).