Abstract
In this paper, we consider the Cauchy problem for the 3D viscous MHD equations, and provide some regularity criteria involving only one directional derivative of the pressure, say ∂3p. In particular, if ∂3p∈Lα(0,T;Lβ(R3))with 2α+3β=2,32≤β≤3, then the solution remains smooth on [0,T].
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