A regularity criterion for the three-dimensional MHD equations in terms of one directional derivative of the pressure

In this work, we will establish a sufficient condition for the regularity criterion to the 3D MHD equations in terms of one directional derivative of the pressure. More precisely, we prove that if ∂π ∂x_3 (x, t) ∈ L 2 1−r  0, T ; · M_(2,3/r) (R^3)  for 0 < r < 1, then the solution (u, b) is regular. We obtain some improvement of the related results in Berselli and Galdi (2002), Cao and Wu (2010), Jia and Zhou (2012), Lin and Du (2013) and Yamazaki (2013).