English

Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

Analysis of PDEs 2012-08-27 v1

Abstract

We present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three. We prove that suitable weak solutions are H\"older continuous near boundary provided that either the scaled Lx,tp,qL^{p,q}_{x,t}-norm of the velocity with 3/p+2/q23/p+2/q\le 2, 2<q<2<q<\infty, or the scaled Lx,tp,qL^{p,q}_{x,t}-norm of the vorticity with 3/p+2/q33/p+2/q\le 3, 2<q<2<q<\infty are sufficiently small near the boundary.

Keywords

Cite

@article{arxiv.1208.4928,
  title  = {Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations},
  author = {Kyungkeun Kang and Jae-Myoung Kim},
  journal= {arXiv preprint arXiv:1208.4928},
  year   = {2012}
}

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22 pages