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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| Format: | Article |
| Language: | English |
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Hindawi Limited
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/456547 |
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doaj-d04da1c71bc742a0a5cc442f3c5dc5022020-11-25T01:45:07ZengHindawi LimitedJournal 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yu-Zhu Wang Zigao Chen |
| spellingShingle |
Yu-Zhu Wang Zigao Chen Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations Journal of Applied Mathematics |
| author_facet |
Yu-Zhu Wang Zigao Chen |
| author_sort |
Yu-Zhu Wang |
| title |
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_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_sort |
regularity criterion for weak solution to the 3d micropolar fluid equations |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2011-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2011/456547 |
| work_keys_str_mv |
AT yuzhuwang regularitycriterionforweaksolutiontothe3dmicropolarfluidequations AT zigaochen regularitycriterionforweaksolutiontothe3dmicropolarfluidequations |
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