A new blow-up criterion for the 2D full compressible Navier-Stokes equations without heat conduction in a bounded domain

Abstract

This paper is to derive a new blow-up criterion for the 2D full compressible Navier-Stokes equations without heat conduction in terms of the density $\ddot{I}$ and the pressure $P$. More precisely, it indicates that in a bounded domain the strong solution exists globally if the norm $\Vert \ddot{I}|{|}_{L^{\infty }(0,t;L^{\infty })}+||P|{|}_{L^{p_0}(0,t;L^{\infty })}<\infty$ for some constant $p_0$ satisfying $1<p_0\le 2$. The boundary condition is imposed as a Navier-slip boundary one and the initial vacuum is permitted. Our result extends previous one which is stated as $\Vert \ddot{I}|{|}_{L^{\infty }(0,t;L^{\infty })}+||P|{|}_{L^{\infty }(0,t;L^{\infty })}<\infty$.

20 pages