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 H4 for the compressible Navier–Stokes equations with the cylinder symmetry in R3 when the initial total energy is sufficiently small. Moreover, the global existence and exponential stability of the classical solution can be also derived.