Global existence in critical spaces for compressible Navier-Stokes equations

Abstract.

We investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible homogeneous Navier-Stokes equations, and one more derivative is needed for the density. We point out a smoothing effect on the velocity and a L ¹-decay on the difference between the density and the constant reference state. The proof lies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.