Large time behavior of solutions to the compressible Navier-Stokes equations around periodic steady states

This paper shows that the strong solution to the compressible Navier-Stokes equation around spatially periodic stationary solution in a periodic layer of Rn(n=2,3) exists globally in time if Reynolds and Mach numbers are sufficiently small. It is proved that the asymptotic leading part of the perturbation is given by a solution to the one-dimensional viscous Burgers equation multiplied by a spatially periodic function when n=2, and by a solution to the two-dimensional heat equation multiplied by a spatially periodic function when n=3.