LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS

doi:10.1016/S0252-9602(17)30056-5

Abstract

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 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).

Key words: local regularity criteria, suitable weak solution, MHD equations

Jae-Myoung KIM. LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS[J].Acta mathematica scientia,Series B, 2017, 37(4): 1033-1047.

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