Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

Kyungkeun Kang; Jae Myoung Kim

doi:10.1016/j.jfa.2013.09.007

Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

Kyungkeun Kang, Jae Myoung Kim

Department of Mathematics

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

13 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 language	English
Pages (from-to)	99-120
Number of pages	22
Journal	Journal of Functional Analysis
Volume	266
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2013.09.007
Publication status	Published - 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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10.1016/j.jfa.2013.09.007

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title = "Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations",

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{\"o}lder 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.",

author = "Kyungkeun Kang and Kim, {Jae Myoung}",

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. ",

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doi = "10.1016/j.jfa.2013.09.007",

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AU - Kang, Kyungkeun

AU - Kim, Jae Myoung

N1 - 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.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

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Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

Abstract

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