BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

doi:10.1016/S0252-9602(17)30096-6

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1632-1638.doi: 10.1016/S0252-9602(17)30096-6

BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

高真圣¹, 谭忠²

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

收稿日期:2016-09-20 修回日期:2017-06-12 出版日期:2017-12-25 发布日期:2017-12-25
通讯作者: Zhong TAN E-mail:ztan85@163.com
作者简介:Zhensheng GAO,gaozhensheng@hqu.edu.cn
基金资助:
The first author is supported by the Natural Science Key Foundation of Universities of Fujian Province (JZ160406) and Natural Science Foundation of Fujian Province (2015J01582).

BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

Zhensheng GAO¹, Zhong TAN²

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2016-09-20 Revised:2017-06-12 Online:2017-12-25 Published:2017-12-25
Contact: Zhong TAN E-mail:ztan85@163.com
Supported by:
The first author is supported by the Natural Science Key Foundation of Universities of Fujian Province (JZ160406) and Natural Science Foundation of Fujian Province (2015J01582).

摘要/Abstract

摘要：

In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in R³. We establish a criterion for possible breakdown of such solutions at a finite time. More precisely, if (u, d) is smooth up to time T provided that ∫₀^T║∇×u(t,·)║_BMO(R³) + ║∇d(t,·)║_L⁴(R³)⁸dt < ∞.

关键词: incompressible, nematic liquid crystal, blow up criterion

Abstract:

Key words: incompressible, nematic liquid crystal, blow up criterion

高真圣, 谭忠. BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS[J]. 数学物理学报(英文版), 2017, 37(6): 1632-1638.

Zhensheng GAO, Zhong TAN. BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1632-1638.

参考文献

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BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

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