We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say,∂3u∈Lp0, T;LqR3, with2/p + 3/q = γ ∈ [1,3/2),3/γ ≤ q ≤ 1/(γ - 1), then the solution is in fact smooth. This improves previous results greatly.
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