Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows
The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocity u0 and small ∇d0. We also g...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/947291 |
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| author | Yong Zhou Jishan Fan Gen Nakamura |
| author_facet | Yong Zhou Jishan Fan Gen Nakamura |
| author_sort | Yong Zhou |
| collection | DOAJ |
| description | The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocity u0 and small ∇d0. We also give a regularity criterion ∇d∈Lp(0,T;Lq(Ω)) (2/q)+(2/p)=1, 2<q≤∞ of the problem with the Dirichlet boundary condition u=0, d=d0 on ∂Ω. |
| format | Article |
| id | doaj-art-310e4c482b2c4950ae347a74fcff6c62 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-310e4c482b2c4950ae347a74fcff6c622025-02-03T01:20:55ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/947291947291Global Strong Solution to the Density-Dependent 2-D Liquid Crystal FlowsYong Zhou0Jishan Fan1Gen Nakamura2Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, ChinaDepartment of Mathematics, Inha University, Incheon 402-751, Republic of KoreaThe initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocity u0 and small ∇d0. We also give a regularity criterion ∇d∈Lp(0,T;Lq(Ω)) (2/q)+(2/p)=1, 2<q≤∞ of the problem with the Dirichlet boundary condition u=0, d=d0 on ∂Ω.http://dx.doi.org/10.1155/2013/947291 |
| spellingShingle | Yong Zhou Jishan Fan Gen Nakamura Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows Abstract and Applied Analysis |
| title | Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows |
| title_full | Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows |
| title_fullStr | Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows |
| title_full_unstemmed | Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows |
| title_short | Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows |
| title_sort | global strong solution to the density dependent 2 d liquid crystal flows |
| url | http://dx.doi.org/10.1155/2013/947291 |
| work_keys_str_mv | AT yongzhou globalstrongsolutiontothedensitydependent2dliquidcrystalflows AT jishanfan globalstrongsolutiontothedensitydependent2dliquidcrystalflows AT gennakamura globalstrongsolutiontothedensitydependent2dliquidcrystalflows |