Global Solutions to Compressible Navier-Stokes Equations With Spherically Symmetric Motion and Free Boundary

TL;DR

This paper proves the global existence of strong and classical solutions to spherically symmetric compressible Navier-Stokes equations with free boundary, handling cases with vacuum and density jumps, and tracking the free boundary over time.

Contribution

It introduces a unified method to establish global regularity for solutions with vacuum and density jumps in spherical symmetry, including free boundary tracking.

Findings

Global existence of strong solutions with vacuum and density jumps.

Unified approach applicable to different vacuum conditions.

Free boundary can be globally tracked over time.

Abstract

This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for spherically symmetric motion. We establish a unified method to track the propagation of regularity of strong and classical solutions which works for the cases when density connects to vacuum continuously and with a jump simultaneously. The result we obtain is able to deal with both strong solutions with physical vacuum for which the sound speed is $1/2$-H\"older continuous across the boundary, and classical solutions with physical vacuum when $ 1 < \gamma < 3 $. In contrast to the previous results of global weak solutions, we track the regularity globally-in-time up to the symmetric center and the moving boundary. In particular, the free boundary can be traced.