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

TL;DR

This paper proves the global existence of classical solutions to the 3D compressible Navier-Stokes equations with slip boundary conditions in exterior domains, allowing large initial density oscillations and vacuum states, using new analytical techniques.

Contribution

It introduces novel methods to establish a priori estimates and demonstrates global solutions under small initial energy, even with large density oscillations and vacuum.

Findings

Global classical solutions exist under small initial energy.

Solutions can handle large density oscillations and vacuum states.

The paper describes the large-time behavior of solutions.

Abstract

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