Low Mach number limit on thin domains

Abstract

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer ${\Omega }_{\delta }=(0,\delta )\times {\mathbb{R}}^2$. We show that the weak solutions in the 3D domain converge strongly to the solution of the 2D incompressible Navier-Stokes equations (Euler equations) when the Mach number $\epsilon$ tends to zero as well as $\delta \to 0$ (and the viscosity goes to zero).