Critical regularity issues for the compressible Navier–Stokes system in bounded domains

Abstract

We are concerned with the barotropic compressible Navier–Stokes system in a bounded domain of mathbb {R}^d (with dge 2). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global well-posedness for small perturbations of a stable constant equilibrium state. Our results rely on new maximal regularity estimates—of independent interest—for the semigroup of the Lamé operator, and of the linearized compressible Navier–Stokes equations.