LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS

Jae-Myoung KIM

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

Acta mathematica scientia, Series B >

2017 , Vol. 37 >Issue 4: 1033 - 1047

DOI: https://doi.org/10.1016/S0252-9602(17)30056-5

Articles

LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS

Jae-Myoung KIM

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Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea

Jae-Myoung KIM,E-mail:cauchy02@naver.com

Received date: 2016-03-04

Revised date: 2016-05-23

Online published: 2017-08-25

Supported by

Jae-Myoung Kim is also partly supported by BK21 PLUS SNU Mathematical Sciences Division and Basic Science Research Program through the National Research Foundation of Korea (NRF) (NRF-2016R1D1A1B03930422).

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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

Cite this article

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 . DOI: 10.1016/S0252-9602(17)30056-5

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