Abstract
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].
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