Regularity criteria for the 3D MHD equations in terms of the pressure

Abstract: In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin’s regularity class, if the pressure p belongs to Lα,γ with 2/α + 3/γ ≤ 2 or the gradient field of pressure ∇p belongs to Lα,γ with 2/α + 3/γ ≤ 3 on [0, T], then the solution remains smooth on [0, T]