  We consider the time-dependent compressible Navier--Stokes equations in the
low Mach number regime in a family of domains $\Omega_\epsilon \subset R^d$
converging in the sense of Mosco to a domain $\Omega \subset R^d$, $d \in
\{2,3\}$. We show the limit is the incompressible Navier--Stokes system in
$\Omega$.
