Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

Kyungkeun Kang, Jae Myoung Kim

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9 Citations (Scopus)

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 Hölder continuous near boundary provided that either the scaled Lx,tp,q-norm of the velocity with 3/. p+. 2/. q≤. 2, 2<. q<. ∞, or the scaled Lx,tp,q-norm of the vorticity with 3/. p+. 2/. q≤. 3, 2<. q<. ∞ are sufficiently small near the boundary.

Original languageEnglish
Pages (from-to)99-120
Number of pages22
JournalJournal of Functional Analysis
Volume266
Issue number1
DOIs
Publication statusPublished - 2014 Jan 1

Bibliographical note

Funding Information:
K. Kangʼs work was partially supported by NRF-2012R1A1A2001373. J.-M. Kimʼs work was partially supported by KRF-2008-331-C00024 and NRF-2009-0088692. The authors wish to express our appreciation to Professor Tai-Peng Tsai for useful comments.

All Science Journal Classification (ASJC) codes

  • Analysis

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