$\mathrm{\Gamma }$-convergence for nearly incompressible fluids

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