We consider the time-dependent compressible Navier–Stokes equations in the low Mach number regime in a family of domains Ωɛ ⊂ Rd converging in the sense of Mosco to a domain Ω ⊂ Rd, d ∈ {2, 3}. We show the limit is the incompressible Navier–Stokes system in Ω.