液晶流体的半强解

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 367-377.

液晶流体的半强解

高真圣¹, 江飞², 王伟伟^{2, 3*}

1.华侨大学数学科学学院福建泉州 361021|
2.福州大学数学与计算机科学学院福州 350108;
3.台湾清华大学数学系台湾新竹 30013

收稿日期:2012-10-19 修回日期:2013-12-20 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
中央高校科研基金(11QZR18)、华侨大学高层次人才科研基金(12BS232)和国家自然科学基金 (11101044, 11271051)资助.

Semi-Strong Solutions to Hydrodynamic Flow of Liquid Crystals

GAO Zhen-Sheng¹, JIANG Fei², WANG Wei-Wei^{2, 3*}

1.School of Mathematical Sciences, Huaqiao University, Fujian Quanzhou 361021;
2.College of Mathematics and Computer Science, Fuzhou University, Fuzhou |350108;
3.Department of Mathematics, Taiwan National Tsing Hua University, Taiwan |Xinzhu 30013

Received:2012-10-19 Revised:2013-12-20 Online:2014-04-25 Published:2014-04-25
Supported by:
中央高校科研基金(11QZR18)、华侨大学高层次人才科研基金(12BS232)和国家自然科学基金 (11101044, 11271051)资助.

摘要/Abstract

摘要：

该文将证明, 即使初始密度在Ω中没有正下界, 二维向列液晶流体存在半强解. 该文主要的新颖点在于新估计||∂, d|_L^4/3(_{I, L²}Ω))不依赖于ρ 的下界, 其中d及ρ 分别表示流体的密度与分子方向.

关键词: 半强解, 流体力学, 液晶, Navier-Stokes方程组

Abstract:

In this paper, we show the existence of semi-strong solutions to hydrodynamic flow of the two-dimensional nematic liquid crystals with small initial data, even though the initial density does not possess the positive lower bound in Ω. The main novelty of the paper lies in the fact that our new estimate of ||∂, d|_L^4/3(_{I, L²}Ω)) is independent of the lower-bound of ρ, where d and ρ represent the director of the molecules and the density of the fluid, respectively.

Key words: Semi-strong solutions, Hydrodynamic flow, Liquid crystals, Navier-Stokes equations

中图分类号:

35Q35

高真圣, 江飞, 王伟伟. 液晶流体的半强解[J]. 数学物理学报, 2014, 34(2): 367-377.

GAO Zhen-Sheng, JIANG Fei, WANG Wei-Wei. Semi-Strong Solutions to Hydrodynamic Flow of Liquid Crystals[J]. Acta mathematica scientia,Series A, 2014, 34(2): 367-377.

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