Exponential stability for the compressible Navier-Stokes equations with the cylinder symmetry in R3

This paper is concerned with the exponential stability in H-1 and H-2 of global weak solutions to the compressible Navier-Stokes equations with the cylinder symmetry in R-3 when the initial total energy is sufficiently small. Such a circular coaxial cylinder symmetric domain in R-3 is an unbounded domain, but under our assumptions on the solutions depending only on one radial spatial variable r is an element of G = {r is an element of R+, 0 < a < r < b < + infinity}, the related domain G to equations is a bounded domain. The Matsumura and Nishida result in R-3 requires the smallness of initial data, while our result does not need the smallness of density. (C) 2010 Elsevier Ltd. All rights reserved.