Local regularity criteria of a suitable weak solution to MHD equations

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are Hölder continuous near boundary provided that the scaled mixed L^p,q_x,t-norm of the velocity vector field with 3/p+2q ≤ 2, 2 < q < ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ? L^p,q_x,t with $1\le \frac{3}{p}+\frac{2}{p}\le \frac{3}{2},3<p<\infty$, the Hausdorff dimension of its singular set is no greater than max {p,q} $\left(\frac{3}{p}+\frac{2}{p}-1\right)$.