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

TL;DR

This paper proves the global existence and exponential decay of solutions to 3D compressible Navier-Stokes equations with large potential forces and slip boundary conditions, even with vacuum states and large density oscillations.

Contribution

It establishes the global existence and decay results for strong/classical solutions under large external forces and vacuum conditions, extending previous results to more complex scenarios.

Findings

Global existence of solutions with small initial energy

Exponential decay of solutions over time

Unbounded density oscillations when initial vacuum is present

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.