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 $\frac{\partial p}{\partial x_3}(x,t)\in L^{\frac{2}{1‐r}}(0,T;{\stackrel{·}{\mathcal{M}}}_{2,\frac{3}{r}}\left({‐{R}}^3\right))\text{for}0<r<1\text{,}$ 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).