Regularity criteria in terms of the pressure for the three-dimensional MHD equations

In this paper, we consider the Cauchy problem for the 3D incompressible MHD equations. A regularity criterion by providing sufficient condition in terms of the pressure is established. More precisely, we show that if p∈Lβ([0,T],Lα(R3)) with 3α+2β⩽74 and 125⩽α⩽4, then any weak solutions (u,b) of the 3D MHD equations is regular on [0,T].