On Regularity for the 3D MHD Equations via One Directional Derivative of the Pressure.

This work establishes a new regularity criterion for the 3D incompressible MHD equations in term of one directional derivative of the pressure (i.e., ∂ 3 P ) on framework of the anisotropic Lebesgue spaces. More precisely, it is proved that for T > 0 , if ∂ 3 P ∈ L β (0 , T ; L α (R x 1 x 2 2 ; L γ (R x 3))) with 2 β + 1 γ + 2 α = k ∈ [ 2 , 3) and 3 k ≤ γ ≤ α ≤ 1 k - 2 , then the corresponding solution (u, b) to the 3D MHD equations is regular on [0, T]. [ABSTRACT FROM AUTHOR]