LOGARITHMICALLY IMPROVED BLOW-UP CRITERION FOR SMOOTH SOLUTIONS TO THE LERAY-α-MAGNETOHYDRODYNAMIC EQUATIONS.

In this paper, the Cauchy problem for the 3D Leray-α-MHD model is investigated. We obtain the logarithmically improved blow-up criterion of smooth solutions for the Leray-α-MHD model in terms of the magnetic field B only in the framework of homogeneous Besov space with negative index. [ABSTRACT FROM AUTHOR]