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

This paper is devoted to the low Mach number limit of weak solutions to the compressible 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 different approach based upon Strichartz's estimates for the linear wave equation in the inviscid case, which improves the convergence result and simplifies the proof. We prove that the velocity field is strongly compact and converges to a global weak solution of the incompressible Navier–Stokes equations.