Global existence of solutions to the compressible Navier-Stokes equations in weighted Besov spaces

Abstract: We prove global existence of solutions to the Cauchy problem for the compressible Navier-Stokes equations in Euclidean spaces, given initial data with small norms in Besov and critical weighted Besov spaces. Global existence and a priori bounds in these spaces are obtained for dimension $d\geq 3$.