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

Abstract

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 = \mbox{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 $ \|H\|_{L^\infty(0, T; \; L^b)}+\| {{\rm{div }}} u\|_{L^1(0, T; \; L^\infty)} < \infty $ for any $ b > 2 $.

Keywords

• full compressible mhd equations
• strong solution
• blow-up criterion