Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L α , γ with 2 α + 3 γ ⩽ 2 or the gradient field of pressure ∇ p belongs to L α , γ with 2 α...

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Bibliographic Details
Published inInternational journal of non-linear mechanics Vol. 41; no. 10; pp. 1174 - 1180
Main Author Zhou, Yong
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2006
Subjects
A priori estimates
MHD equations
Regularity criterion
35B65
76D05
Regularity criterion
MHD equations
35Q35
A priori estimates
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Summary:In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L α , γ with 2 α + 3 γ ⩽ 2 or the gradient field of pressure ∇ p belongs to L α , γ with 2 α + 3 γ ⩽ 3 on [ 0 , T ] , then the solution remains smooth on [ 0 , T ] .
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2006.12.001