A new regularity criterion for the 3D incompressible MHD equations in terms of one component of the gradient of pressure

In this paper we study the global regularity issue for the 3D incompressible MHD equations. It is proved that if the pressure P satisfies ∂ 3 P ∈ L β ( 0 , T ; L μ ( R 3 ) ) , with 2 β + 3 μ ≤ 2 , 3 ≤ μ < + ∞ and 1 < β < + ∞ , then the corresponding weak solution ( u , b ) is regular on  [ 0 , T ] .