Exponential stability for the compressible Navier–Stokes equations with the cylinder symmetry in R3R3

This paper is concerned with the exponential stability in H1H1 and H2H2 of global weak solutions to the compressible Navier–Stokes equations with the cylinder symmetry in R3R3 when the initial total energy is sufficiently small. Such a circular coaxial cylinder symmetric domain in R3R3 is an unbounded domain, but under our assumptions on the solutions depending only on one radial spatial variable r∈G={r∈R+,0