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

Kyungkeun Kang, Jae Myoung Kim

Research output: Contribution to journalArticle

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

Fingerprint

Regularity Criterion
Magnetohydrodynamic Equations
Slip Boundary Condition
Magnetohydrodynamics
Half-space
Bounded Domain
Boundary conditions
Weak Solution
Slip
Velocity Field
Magnetic Field
Magnetic fields
Three-dimensional
Demonstrate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

@article{d15d6ae9a6474f0dbb0c4c26ee1da2a5,
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.",
author = "Kyungkeun Kang and Kim, {Jae Myoung}",
year = "2012",
month = "7",
day = "15",
doi = "10.1016/j.jde.2012.04.007",
language = "English",
volume = "253",
pages = "764--794",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "2",

}

Regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space. / Kang, Kyungkeun; Kim, Jae Myoung.

In: Journal of Differential Equations, Vol. 253, No. 2, 15.07.2012, p. 764-794.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space

AU - Kang, Kyungkeun

AU - Kim, Jae Myoung

PY - 2012/7/15

Y1 - 2012/7/15

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.

UR - http://www.scopus.com/inward/record.url?scp=84860608665&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860608665&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2012.04.007

DO - 10.1016/j.jde.2012.04.007

M3 - Article

AN - SCOPUS:84860608665

VL - 253

SP - 764

EP - 794

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -