Free boundary value problem for the cylindrically symmetric compressible navier-stokes equations with density-dependent viscosity

In this paper, we investigate the free boundary value problem (FBVP) for the cylindrically symmetric isentropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.