On the low Mach number limit of compressible flows in exterior moving domains

Abstract

Abstract. We study the incompressible limit of solutions to the compressible barotropic Navier-Stokes system in the exterior of a bounded domain undergoing a simple translation. The problem is reformulated using a change of coordinates to fixed exterior domain. Using the spectral analysis of the wave propagator, the dispersion of acoustic waves is proved by the means of the RAGE theorem. The solution to the incompressible Navier-Stokes equations is identified as a limit.

Motion of Fluids in the Moving Domain

“…The question of weak-strong uniqueness and existence of the strong solution in L 2 case was shown in [14]. There are also a few results of the problem of singular limits in a moving domain, see [6,8].…”

Low stratification of a heat-conducting fluid in time-dependent domain

“…In the barotropic case, the existence theory of global weak solution was proved by Feireisl et al [14,19] for the Dirichlet and Navier type of boundary conditions, respectively. Moreover, in the framework of weak solutions the singular limit (low Mach number limit) in the case of moving domain was investigated by Feireisl et al in [18,20].…”