Stability with respect to domain of the low Mach number limit of compressible viscous fluids (Q2857741)

This paper concerns the incompressible limit of solutions to the barotropic Navier-Stokes system when the Mach number \(\epsilon\rightarrow0\). And the fluid is confined in exterior spatial domains \(\Omega_\epsilon\) with completely slip boundary conditions, where the physical domains \(\Omega_\epsilon\) are allowed to change their shape together with the Mach number \(\epsilon\). Based on spectral theory for the corresponding acoustic wave propagator (Neumann Laplacian) and delicate estimates of the associated Helmholtz projections, it is shown that as \(\epsilon\rightarrow0\) the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes system on a limit domain.