Inviscid incompressible limits on expanding domains

We consider the inviscid incompressible limit of the compressible Navier–Stokes system on a large domain, the radius of which becomes infinite in the asymptotic limit. We show that the limit solutions satisfy the incompressible Euler system on the whole physical space R³ as long as the radius of the domain is larger than the speed of acoustic waves inversely proportional to the Mach number. The rate of convergence is estimated in terms of the Mach and Reynolds numbers and the radius of the family of spatial domains.