This paper is concerned with large time behavior of solutions to the compressible Navier–Stokes equations in an infinite layer of [Formula: see text] under slip boundary condition. It is shown that if the initial data is sufficiently small, the global solution uniquely exists and the large time behavior of the solution is described by a superposition of one-dimensional diffusion waves.

The large time behavior of solutions to the compressible Navier‐Stokes equations around the motionless state is considered in a cylinder under the slip boundary condition. It is shown that if the initial data are sufficiently small, the global solution uniquely exists and the large time behavior of the solution is described by a superposition of one‐dimensional nonlinear diffusion waves and a diffusive rigid rotation.