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We are concerned with the global existence of classical solutions to thebarotropic compressible Navier-Stokes equations with slip boundary condition ina three-dimensional (3D) exterior domain. We demonstrate that the classicalsolutions exists globally in time provided that the initial total energy issuitably small. It is worth noting that the initial density is allowed to havelarge oscillations and contain vacuum states. For our purpose, some newtechniques and methods are adopted to obtain necessary a priori estimates,especially the estimates on the boundary. Moveover, we also give the large-timebehavior of the classical solutions what we have gotten.

Global Classical Solutions to the Compressible Navier-Stokes Equations with Slip Boundary Conditions in 3D Exterior Domains