Local well-posedness of strong solutions to the compressible Navier-Stokes equations with degenerate viscosities and far field vacuum in 3D exterior domains

TL;DR

This paper proves the local existence and uniqueness of strong solutions to the 3D compressible Navier-Stokes equations with degenerate viscosities and far-field vacuum in exterior domains, overcoming boundary and vacuum challenges.

Contribution

It establishes local well-posedness for solutions with density-dependent viscosities and far-field vacuum, independent of the gas coefficient gamma.

Findings

Successfully handles boundary terms and vacuum issues

Provides a method independent of gamma for viscosity selection

Ensures strong solutions exist locally in time

Abstract

The isentropic compressible Navier-Stokes system subject to the Navier-slip boundary conditions is considered in a general three-dimensional exterior domain. For the density approaches far-field vacuum initially and the viscosities are power functions of the density({\rho}^{\delta} with 0 < {\delta}< 1), the local well-posedness of strong solutions is established in this paper. In particular, the method we adopt can not only simultaneously handle the difficulties caused by boundary terms and far-field vacuum, but also make the selection of {\delta} independent of the gas coefficient {\gamma}.