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.
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