One new blow-up criterion for the two-dimensional full compressible magnetohydrodynamic equations

This paper concerns the blow-up criterion for two-dimensional (2D) viscous, compressible, and heat conducting magnetohydrodynamic(MHD) flows. When the magnetic field $H$ satisfies the perfect conducting boundary condition $H\cdot n=\text{curl}H=0$, we prove that for the initial boundary value problem of the two-dimensional full compressible MHD flows with initial density allowed to vanish, the strong solution exists globally provided $\Vert H{\Vert }_{L^{\mathrm{\infty }}(0,T;L^b)}+\Vert \mathrm{d}\mathrm{i}\mathrm{v}u{\Vert }_{L^1(0,T;L^{\mathrm{\infty }})}<\mathrm{\infty }$ for any $b>2$.