A regularity criterion for the 3D incompressible magneto-hydrodynamics equations

The paper is dedicated to study of the regularity criterion for weak solutions to the 3D incompressible MHD equations. Employing the Littlewood-Paley decomposition, we show that if ∇˜u˜=(∂1u˜,∂2u˜)∈Ls1([0,T);B˙r1,2r130(R3)), 2s1+3r1=2, 32