Large time behavior of solutions to the compressible Navier–Stokes equations around periodic steady states. (March 2017) - Enomoto, Shota
Abstract: This paper shows that the strong solution to the compressible Navier–Stokes equation around spatially periodic stationary solution in a periodic layer of R n ( 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 .