Local regularity criteria of a suitable weak solution to MHD equations

Abstract

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 Lp,qx,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 ɛ Lp,qx,t with 1≤3p+2p≤32,3<p<∞, the Hausdorff dimension of its singular set is no greater than max {p,q} (3p+2p-1).