Abstract
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<r1≤∞ and ∇˜b˜=(∂1b˜,∂2b˜)∈Ls2([0,T);B˙r2,2r230(R3)), 2s2+3r2=2, 32<r2≤∞, then the solutions to the MHD actually is smooth on (0,T).
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