Global Classical Solutions to the Full Compressible Navier-Stokes System in 3D Exterior Domains

TL;DR

This paper proves the existence of unique, global classical solutions to the full compressible Navier-Stokes system in 3D exterior domains, allowing for initial vacuum states and large oscillations, a first in this setting.

Contribution

It establishes the first existence and uniqueness results for classical solutions of the FNS system in 3D exterior domains with initial vacuum and large oscillations.

Findings

Global classical solutions exist under small energy initial data.

Solutions accommodate initial vacuum states.

First such results in 3D exterior domains.

Abstract

The full compressible Navier-Stokes system (FNS) describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid in a three-dimensional (3D) exterior domain is studied. For the initial-boundary-value problem with the slip boundary conditions on the velocity and the Neumann one on the temperature, it is shown that there exists a unique global classical solutions with the initial data which are of small energy but possibly large oscillations. In particular, both the density and temperature are allowed to vanish initially. This is the first result about classical solutions of FNS system in 3D exterior domain.