Logarithmically improved blow-up criterion for smooth solutions to the leray-α-magnetohydrodynamic equations

Abstract

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.