Regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space

Kyungkeun Kang, Jae Myoung Kim

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We study three-dimensional incompressible magnetohydrodynamic equations in bounded domains or a half space. We present new regularity criteria of weak solutions: a pair of weak solutions, (u, b), become regular if u satisfies Serrin's type conditions when we consider no-slip or slip boundary conditions for the velocity field, u, and slip boundary conditions for the magnetic field, b, in either bounded domains or a half space. In addition, in the case of a half-space with no-slip boundary conditions for u and slip boundary conditions for b, we demonstrate that, if tangential components of u and normal component of b satisfy Serrin's type conditions, then a pair of weak solutions, (u, b), become regular.

Original languageEnglish
Pages (from-to)764-794
Number of pages31
JournalJournal of Differential Equations
Volume253
Issue number2
DOIs
Publication statusPublished - 2012 Jul 15

Bibliographical note

Funding Information:
K. Kang’s work was partially supported by NRF-2011-0028951. J.-M. Kim’s work was partially supported by KRF-2008-331-C00024 and NRF-2009-0088692.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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