Incompressible limit for a viscous compressible fluid

We prove various asymptotic results concerning global (weak) solutions of compressible isentropic Navier-Stokes equations. More precisely, we show various results establishing the convergence, as the density becomes constant and the Mach number goes to 0, towards solutions of incompressible models (Navier-Stokes or Euler equations). Most of these results are global in time and without size restriction on the initial data. We also observe rigorously the linearized system around constant flows.