STABILITY WITH RESPECT TO DOMAIN OF THE LOW MACH NUMBER LIMIT OF COMPRESSIBLE VISCOUS FLUIDS

Abstract

We study the asymptotic limit of solutions to the barotropic Navier–Stokes system, when the Mach number is proportional to a small parameter ε → 0 and the fluid is confined to an exterior spatial domain Ωε that may vary with ε. As ε → 0, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier–Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.