Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows
In this paper, we study the regularity criterion for the local smooth solution of the 3D nematic liquid crystal flows. More precisely, it is proved the smooth solution u,d can be extended beyond T provided that ∫0T∇huhB˙∞,∞0+∇dB˙∞,∞02/1+log1+∇uB˙∞,∞0+∇dB˙∞,∞0dt<∞ or ∫0T∇huhB˙∞,∞−r4/3−2r+∇dB˙∞,∞02...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4454497 |
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| _version_ | 1850210143083429888 |
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| author | Ruirui Wang Qiang Mu Yulei Wang Qiang Li |
| author_facet | Ruirui Wang Qiang Mu Yulei Wang Qiang Li |
| author_sort | Ruirui Wang |
| collection | DOAJ |
| description | In this paper, we study the regularity criterion for the local smooth solution of the 3D nematic liquid crystal flows. More precisely, it is proved the smooth solution u,d can be extended beyond T provided that ∫0T∇huhB˙∞,∞0+∇dB˙∞,∞02/1+log1+∇uB˙∞,∞0+∇dB˙∞,∞0dt<∞ or ∫0T∇huhB˙∞,∞−r4/3−2r+∇dB˙∞,∞02/1+log1+∇uB˙∞,∞0+∇dB˙∞,∞0dt<∞,0≤r≤1. |
| format | Article |
| id | doaj-art-972fbf09e6c5446bb7f145bec1909159 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-972fbf09e6c5446bb7f145bec19091592025-08-20T02:09:51ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4454497Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal FlowsRuirui Wang0Qiang Mu1Yulei Wang2Qiang Li3School of Mathematics and StatisticsSchool of Mathematics and StatisticsSchool of Mathematics and StatisticsSchool of Mathematics and StatisticsIn this paper, we study the regularity criterion for the local smooth solution of the 3D nematic liquid crystal flows. More precisely, it is proved the smooth solution u,d can be extended beyond T provided that ∫0T∇huhB˙∞,∞0+∇dB˙∞,∞02/1+log1+∇uB˙∞,∞0+∇dB˙∞,∞0dt<∞ or ∫0T∇huhB˙∞,∞−r4/3−2r+∇dB˙∞,∞02/1+log1+∇uB˙∞,∞0+∇dB˙∞,∞0dt<∞,0≤r≤1.http://dx.doi.org/10.1155/2022/4454497 |
| spellingShingle | Ruirui Wang Qiang Mu Yulei Wang Qiang Li Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows Journal of Mathematics |
| title | Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows |
| title_full | Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows |
| title_fullStr | Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows |
| title_full_unstemmed | Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows |
| title_short | Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows |
| title_sort | two logarithmically improved regularity criteria for the 3d nematic liquid crystal flows |
| url | http://dx.doi.org/10.1155/2022/4454497 |
| work_keys_str_mv | AT ruiruiwang twologarithmicallyimprovedregularitycriteriaforthe3dnematicliquidcrystalflows AT qiangmu twologarithmicallyimprovedregularitycriteriaforthe3dnematicliquidcrystalflows AT yuleiwang twologarithmicallyimprovedregularitycriteriaforthe3dnematicliquidcrystalflows AT qiangli twologarithmicallyimprovedregularitycriteriaforthe3dnematicliquidcrystalflows |