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

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 $\rho$ and the pressure $P$. More precisely, it indicates that in a bounded domain the strong solution exists globally if the norm $\mathrm{\parallel }\rho \mathrm{\mid }{\mathrm{\mid }}_{L^{\mathrm{\infty }}(0,t;L^{\mathrm{\infty }})}+\mathrm{\mid }\mathrm{\mid }P\mathrm{\mid }{\mathrm{\mid }}_{L^{p_0}(0,t;L^{\mathrm{\infty }})}<\mathrm{\infty }$ 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 $\mathrm{\parallel }\rho \mathrm{\mid }{\mathrm{\mid }}_{L^{\mathrm{\infty }}(0,t;L^{\mathrm{\infty }})}+\mathrm{\mid }\mathrm{\mid }P\mathrm{\mid }{\mathrm{\mid }}_{L^{\mathrm{\infty }}(0,t;L^{\mathrm{\infty }})}<\mathrm{\infty }$.