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

摘要

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.