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

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 $\Vert {\rho }_0{\Vert }_{L^{\infty }(\Omega )}$ and $\Vert {\rho }_0|u_0{|}^5{\Vert }_{L^1(\Omega )}$ are sufficient small.