Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions

We study here the limit of global weak solutions of the compressible Navier-Stokes equations (in the isentropic regime) in a bounded domain, with Dirichlet boundary conditions on the velocity, as the Mach number goes to 0. We show that the velocity converges weakly in L-2 to a global weak solution of the incompressible Navier-Stokes equations. Moreover, the convergence in L-2 is strong under some geometrical assumption on Omega. (C) Elsevier, Paris.