Global existence and exponential stability of solutions in H4 for the compressible Navier-Stokes equations with the cylinder symmetry

This paper is concerned with the global existence and exponential stability of solutions in H-4 for the compressible Navier-Stokes equations with the cylinder symmetry in R-3 when the initial total energy is sufficiently small. Moreover, the global existence and exponential stability of the classical solution can be also derived. (C) 2010 Elsevier Inc. All rights reserved.