Strong solutions of the Navier-Stokes equations for isentropic compressible fluids

We study strong solutions of the isentropic compressible Navier-Stokes equations in a domain Q subset of R-3. We first prove the local existence of unique strong solutions provided that the initial data rho(0) and u(0) satisfy a natural compatibility condition. The important point in this paper is that we allow the initial vacuum: the initial density may vanish in an open subset of Q. We then prove a new uniqueness result and stability result. Our results are valid for unbounded domains as well as bounded ones. (C) 2003 Elsevier Science (USA). All rights reserved.