Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

Regularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some T>0, if ∫0T∥vx3∥Lϱρdt<∞, where 3/ϱ+2/ρ≤1 and ϱ≥3, then the solution (v,w) can be extended smoothly beyond t=T. The derivative vx3 can be substituted with any directional derivative of v....

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Main Authors: Yu-Zhu Wang, Zigao Chen
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2011/456547
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author Yu-Zhu Wang
Zigao Chen
author_facet Yu-Zhu Wang
Zigao Chen
author_sort Yu-Zhu Wang
collection DOAJ
description Regularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some T>0, if ∫0T∥vx3∥Lϱρdt<∞, where 3/ϱ+2/ρ≤1 and ϱ≥3, then the solution (v,w) can be extended smoothly beyond t=T. The derivative vx3 can be substituted with any directional derivative of v.
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institution DOAJ
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publishDate 2011-01-01
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series Journal of Applied Mathematics
spelling doaj-art-d04da1c71bc742a0a5cc442f3c5dc5022025-08-20T03:19:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/456547456547Regularity Criterion for Weak Solution to the 3D Micropolar Fluid EquationsYu-Zhu Wang0Zigao Chen1School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaSchool of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaRegularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some T>0, if ∫0T∥vx3∥Lϱρdt<∞, where 3/ϱ+2/ρ≤1 and ϱ≥3, then the solution (v,w) can be extended smoothly beyond t=T. The derivative vx3 can be substituted with any directional derivative of v.http://dx.doi.org/10.1155/2011/456547
spellingShingle Yu-Zhu Wang
Zigao Chen
Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
Journal of Applied Mathematics
title Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
title_full Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
title_fullStr Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
title_full_unstemmed Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
title_short Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
title_sort regularity criterion for weak solution to the 3d micropolar fluid equations
url http://dx.doi.org/10.1155/2011/456547
work_keys_str_mv AT yuzhuwang regularitycriterionforweaksolutiontothe3dmicropolarfluidequations
AT zigaochen regularitycriterionforweaksolutiontothe3dmicropolarfluidequations