Global Strong Solutions to the Three-Dimensional Axisymmetric Compressible Navier-Stokes Equations with Large Initial Data and Vacuum

Abstract: This paper investigates the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain that excludes the axis. For initial density allowed to vanish, the global existence and large time asymptotic behavior of strong and weak solutions are established, provided the shear viscosity is a positive constant and the bulk one is a power function of density with the power bigger than four-thirds. It should be noted that this result is obtained without any restrictions on the size of initial data.