On Compressible Navier-Stokes Equations Subject to Large Potential Forces with Slip Boundary Conditions in 3D Bounded Domains

Abstract

We deal with the barotropic compressible Navier-Stokes equations subject to large external potential forces with slip boundary condition in a 3D simply connected bounded domain, whose smooth boundary has a finite number of 2D connected components. The global existence of strong or classical solutions to the initial boundary value problem of this system is established provided the initial energy is suitably small. Moreover, the density has large oscillations and contains vacuum states. Finally, we show that the global strong or classical solutions decay exponentially in time to the equilibrium in some Sobolev's spaces, but the oscillation of the density will grow unboundedly in the long run with an exponential rate when the initial density contains vacuum states.