Asymptotic behavior for cylindrically symmetric nonbarotropic flows in exterior domains with large data

Abstract

We study the initial–boundary value problem for the compressible Navier–Stokes equations describing the cylindrically symmetric motion of a viscous nonbarotropic fluid in the domain exterior to a ball in R3. The global solution is proved to exist uniquely and be asymptotically stable as time tends to infinity for large initial data. Moreover, the density and temperature are shown to be bounded from above and below uniformly in both time and space. Our analysis is based on nonlinear energy methods.