A BLOW-UP CRITERION FOR 3D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM

摘要

This paper is concerned with a blow-up criterion of strong solutions for three-dimensional compressible isentropic magnetohydrodynamic equations with vacuum. It is shown that if the density and velocity satisfy ‖P /b>‖L~∞(O,T;L~∞>) +‖u‖L~s(O,T;L_w~r)<∞ where 2/s+3/r%le; 1, 3 < r ≥ ∞ and L_w~r?L~r denotes the weak L~r-space, then the strong solutions to the Cauchy problem of the compressible magnetohydrodynamic equations can exist globally over [O, T].