Low Mach number limit of viscous compressible flows in the whole space

Abstract

This paper is devoted to the low Mach number limit of weak solutions to the com-pressible Navier{Stokes equations for isentropic fluids in the whole space Rd (d = 2 or 3). This problem was investigated by P. L. Lions and N. Masmoudi. We present here a dierent approach based upon Strichartz’s estimates for the linear wave equa-tion in the inviscid case, which improves the convergence result and simplies the proof. We prove that the velocity eld is strongly compact and converges to a global weak solution of the incompressible Navier{Stokes equations.