In this paper we consider the regularitycriteria for the solution to the 3D MHD equations. It is provedthat if the gradient of the velocity field belongs toLα,γ with 2/α+3/γ ≤ 2 or thevelocity field belongs to Lα,γ with2/α+3/γ ≤ 1 on $[0,T]$, then the solution remainssmooth on $[0,T]$. The significance is that there are norestriction on the magnetic field. Moreover, the norms ||||_Lα,γ and \|\|u\|\|_Lα,γ arescaling dimension zero for 2/α+3/γ=2 and2/α+3/γ=1 respectively.
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Yong Zhou (2005) studied this question.