A blow-up criterion of strong solutions to the 3D compressible MHD equations with vacuum

In this paper, we prove a blow-up criterion of strong solutions to 3D viscous isentropic compressible magnetohydrodynamic equations. It is shown that if ρ and H satisfy ‖ρ‖L∞(0,T;L∞)+‖H‖L∞(0,T;Lr)<∞, for any 24/5≤r≤∞ and 3μ>λ, then the strong solutions to the Cauchy problem of the compressible magnetohydrodynamic equations can exist globally on [0,T]. In addition, initial vacuum is allowed.