A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum.

In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy (∥ ρ ∥ L ∞ (0 , T ; L ∞) + ∥ u ∥ C ([ 0 , T ] ; L 3) < ∞) , then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over [ 0 , T ] . Notably, our analysis accommodates the presence of an initial vacuum. [ABSTRACT FROM AUTHOR]