| 三维液晶方程一个与水平速度相关的改进正则性准则 |
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| 引用本文： | 陈晓莉,查秀娟. 三维液晶方程一个与水平速度相关的改进正则性准则[J]. 数学研究及应用, 2021, 41(6): 607-614 |
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| 作者姓名： | 陈晓莉 查秀娟 |
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| 作者单位： | 江西师范大学数学与统计学院, 江西 南昌 330022 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11961032; 11971209), 江西省自然科学基金(Grant No.20191BAB201003). |
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| 摘 要： | 根据速度的水平分量$u_h$的垂直导数,本文研究了3维液晶方程的整体正则性,具体地,当速度的水平分量$u_h$的垂直导数满足$partial_3u_hin L^p(0,T; R^3), frac{2}{p}+frac{3}{q}le frac{3}{2}$, $2le ple infty$,则局部强解$(u,d)$可以光滑的延拓出$t=T$.
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| 关 键 词： | 液晶流 正则性准则 局部强解 |
| 收稿时间： | 2020-10-18 |
| 修稿时间： | 2021-06-26 |
A Refined Regularity Criterion for $3$D Liquid Crystal Equations Involving Horizontal Velocity |
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| Xiaoli CHEN,Xiujuan ZHA. A Refined Regularity Criterion for $3$D Liquid Crystal Equations Involving Horizontal Velocity[J]. Journal of Mathematical Research with Applications, 2021, 41(6): 607-614 |
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| Authors: | Xiaoli CHEN Xiujuan ZHA |
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| Affiliation: | School of Mathematics and Statistics, Jiangxi Normal University, Jiangxi 330022, P. R. China |
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| Abstract: | This note investigates the global regularity of $3$D liquid crystal equations in terms of the vertical derivative of $u_h$. More precisely, we prove that if the vertical derivative of the horizontal velocity component $u_h$ satisfies $pa_3u_hin L^p(0,T; R^3)$ with $frac{2}{p}+frac{3}{q}le frac{3}{2}$, $2le ple infty$, then the local strong solution $(u,d)$ can be smoothly extended beyond $t=T$. |
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| Keywords: | liquid crystal flow regularity criterion local strong solution |
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