$\Gamma$-convergence for nearly incompressible fluids

Abstract

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 $\Omega$.