This paper is concerned with the initial boundary value problem for the three-dimensional Navier-Stokes equations with density-dependent viscosity. The cylindrically symmetric strong solution is shown to exist globally in time and tend to the equilibrium state exponentially as time grows up.
Jian Liu. Ruxu Lian. "Global Existence of the Cylindrically Symmetric Strong Solution to Compressible Navier-Stokes Equations." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/728715