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

Kyungkeun Kang; Jae Myoung Kim

doi:10.1016/j.jde.2012.04.007

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

Kyungkeun Kang, Jae Myoung Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

23 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 language	English
Pages (from-to)	764-794
Number of pages	31
Journal	Journal of Differential Equations
Volume	253
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2012.04.007
Publication status	Published - 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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10.1016/j.jde.2012.04.007

Cite this

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title = "Regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space",

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.",

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N2 - 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.

AB - 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.

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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