Global existence and exponential stability of solutions in H~4 for the compressible Navier-Stokes equations with the cylinder symmetry

摘要

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.