Blow-up criterion for two-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows

This paper establishes a blow-up criterion for the two-dimensional (2D) viscous, compressible, and heat conducting magnetohydrodynamic(MHD) flows. It is essentially shown that for the initial boundary value problem of the 2D full compressible MHD flows with initial density allowed to vanish, the strong solution exists globally if the divergence of velocity satisfies ‖divu‖L1(0,T;L∞)<∞. In particular, the criterion is independent of both the temperature and the magnetic field and is just the same as that of the full compressible Navier–Stokes equations.