A regularity criterion of strong solutions to the 2D compressible magnetohydrodynamic equations

This paper establishes a regularity criterion of strong solutions to the two-dimensional compressible magnetohydrodynamic (MHD) flows. The criterion depends on the density, but is independent of the velocity and the magnetic field. More precisely, once the strong solutions blow up, the L∞-norm for the density tends to infinity. In particular, the vacuum in the solutions is allowed.