Global strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain

TL;DR

This paper proves the global existence of strong solutions to the 3D full compressible Navier-Stokes equations with vacuum in a bounded domain, under specific viscosity and initial data conditions.

Contribution

It establishes the first global well-posedness result for strong solutions with vacuum in a bounded domain for this system.

Findings

Global strong solutions exist under small initial data conditions.

The viscosity coefficients must satisfy 7λ > 9μ.

The solutions are valid for initial densities and velocities satisfying certain smallness conditions.

Abstract

In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain $\Omega\subset \mathbb{R}^3$ by the bootstrap argument provided that the viscosity coefficients $\lambda$ and $\mu$ satisfy that $7\lambda>9\mu$ and the initial data $\rho_0$ and $u_0$ satisfy that $\|\rho_0\|_{L^\infty(\Omega)}$ and $\|\rho_0|u_0|^5\|_{L^1(\Omega)}$ are sufficient small.