  We investigate the barotropic compressible Navier-Stokes equations with slip
boundary conditions in a three-dimensional (3D) simply connected bounded
domain, whose smooth boundary has a finite number of two-dimensional connected
components. For any adiabatic exponent bigger than one, after discovering some
new estimates on boundary integrals related to the slip boundary condition, we
prove that both the weak and classical solutions to the initial-boundary-value
problem of this system exist globally in time provided the initial energy is
suitably small. Moreover, the density has large oscillations and contains
vacuum states. Finally, it is also shown that for the classical solutions, the
oscillation of the density will grow unboundedly in the long run with an
exponential rate provided vacuum appears (even at a point) initially. This is
the first result concerning the global existence of classical solutions to the
compressible Navier-Stokes equations with density containing vacuum states
initially for general 3D bounded smooth domains.
