MHD Equations with Regularity in One Direction

We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, ∂3u∈Lp0, T;LqR3, with 2/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