Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in 3D

TL;DR

This paper proves the local existence and uniqueness of strong solutions for the 3D free boundary problem of the full compressible Navier-Stokes equations, accommodating more general initial conditions and removing symmetry assumptions.

Contribution

It extends previous results by removing spherical symmetry and allowing more general initial density and temperature profiles in the analysis.

Findings

Established local-in-time existence of strong solutions.

Proved uniqueness of solutions under given conditions.

Extended previous results to more general initial data.

Abstract

In this paper we establish the local-in-time existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in three-dimensional space. The vanishing density and temperature condition is imposed on the free boundary, which captures the motions of the non-isentropic viscous gas surrounded by vacuum with bounded entropy. We also assume some proper decay rates of the density towards the boundary and singularities of derivatives of the temperature across the boundary on the initial data, which coincides with the physical vacuum condition for the isentropic flows. This extends the previous result of Liu [ArXiv:1612.07936] by removing the spherically symmetric assumption and considering more general initial density and temperature profiles.