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 sp
ace R-d (d = 2 or 3). This problem was investigated by P. L. Lions and N. M
asmoudi. We present here a different approach based upon Strichartz's estim
ates for the linear wave equation in the inviscid case, which improves the
convergence result and simplifies the proof. We prove that the velocity fie
ld is strongly compact and converges to a global weak solution of the incom
pressible Navier-Stokes equations.