Regularity of solutions to 3-D nematic liquid crystal flows
In this note we consider the regularity of solutions to 3-D nematic liquid crystal flows, we prove that if either $uin L^{q}(0,T;L^p(mathbb{R}^3))$, $frac{2}{q}+frac{3}{p}leq1$, $3<pleqinfty$; or $uin L^{alpha}(0,T;L^{eta}(mathbb{R}^3))$, $frac{2}{alpha}+frac{3}{eta}leq 2$, $frac{3}{2}&...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2010-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/173/abstr.html |
| _version_ | 1819117111379755008 |
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| author | Qiao Liu Shangbin Cui |
| author_facet | Qiao Liu Shangbin Cui |
| author_sort | Qiao Liu |
| collection | DOAJ |
| description | In this note we consider the regularity of solutions to 3-D nematic liquid crystal flows, we prove that if either $uin L^{q}(0,T;L^p(mathbb{R}^3))$, $frac{2}{q}+frac{3}{p}leq1$, $3<pleqinfty$; or $uin L^{alpha}(0,T;L^{eta}(mathbb{R}^3))$, $frac{2}{alpha}+frac{3}{eta}leq 2$, $frac{3}{2}< etaleqinfty$, then the solution $(u,d)$ is regular on $(0,T]$. |
| first_indexed | 2024-12-22T05:27:47Z |
| format | Article |
| id | doaj.art-1b49aed925d844f1b774d8cadc8e8e50 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T05:27:47Z |
| publishDate | 2010-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1b49aed925d844f1b774d8cadc8e8e502022-12-21T18:37:32ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-12-012010173,15Regularity of solutions to 3-D nematic liquid crystal flowsQiao LiuShangbin CuiIn this note we consider the regularity of solutions to 3-D nematic liquid crystal flows, we prove that if either $uin L^{q}(0,T;L^p(mathbb{R}^3))$, $frac{2}{q}+frac{3}{p}leq1$, $3<pleqinfty$; or $uin L^{alpha}(0,T;L^{eta}(mathbb{R}^3))$, $frac{2}{alpha}+frac{3}{eta}leq 2$, $frac{3}{2}< etaleqinfty$, then the solution $(u,d)$ is regular on $(0,T]$.http://ejde.math.txstate.edu/Volumes/2010/173/abstr.htmlLiquid crystal flowinitial value problemregularity of solutions |
| spellingShingle | Qiao Liu Shangbin Cui Regularity of solutions to 3-D nematic liquid crystal flows Electronic Journal of Differential Equations Liquid crystal flow initial value problem regularity of solutions |
| title | Regularity of solutions to 3-D nematic liquid crystal flows |
| title_full | Regularity of solutions to 3-D nematic liquid crystal flows |
| title_fullStr | Regularity of solutions to 3-D nematic liquid crystal flows |
| title_full_unstemmed | Regularity of solutions to 3-D nematic liquid crystal flows |
| title_short | Regularity of solutions to 3-D nematic liquid crystal flows |
| title_sort | regularity of solutions to 3 d nematic liquid crystal flows |
| topic | Liquid crystal flow initial value problem regularity of solutions |
| url | http://ejde.math.txstate.edu/Volumes/2010/173/abstr.html |
| work_keys_str_mv | AT qiaoliu regularityofsolutionsto3dnematicliquidcrystalflows AT shangbincui regularityofsolutionsto3dnematicliquidcrystalflows |