## LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS

**Jae-Myoung KIM;Department of Mathematical Sciences, Seoul National University;**

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 H¨older continuous near boundary provided that the scaled mixed L_(x,t)~(p,q) -norm of the velocity vector field with 3/p + 2/q ≤ 2,2 q ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ L_(x,t)~(p,q) with 1≤3/p+2/q≤3/2, 3 p ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}(3/p+2/q-1).

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【Fund】： partly supported by BK21 PLUS SNU Mathematical Sciences Division and Basic Science Research Program through the National Research Foundation of Korea(NRF)(NRF-2016R1D1A1B03930422)

【CateGory Index】： O175

**local regularity criteria****suitable weak solution****MHD equations**【Fund】： partly supported by BK21 PLUS SNU Mathematical Sciences Division and Basic Science Research Program through the National Research Foundation of Korea(NRF)(NRF-2016R1D1A1B03930422)

【CateGory Index】： O175

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