Global Existence and Incompressible Limit for the Three-Dimensional Axisymmetric Compressible Navier-Stokes Equations with Large Bulk Viscosity and Large Initial Data

Abstract: In this paper, we study the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain excluding the axis. We establish the global existence and exponential decay of weak, strong, and classical solutions with large initial data and vacuum, under the assumption that the bulk viscosity coefficient is sufficiently large. Moreover, we demonstrate that as the bulk viscosity coefficient tends to infinity, the solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations.