Singularity and existence for a wave system of nematic liquid crystals

被引：18

作者：

Chen, Geng ^{[1
]}

Zheng, Yuxi ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 398卷 / 01期

关键词：

Liquid crystal; Singularity; Wave equations; WEAK SOLUTIONS; CONSERVATIVE SOLUTIONS; EQUATION; REGULARITY; MAPS;

D O I：

10.1016/j.jmaa.2012.08.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the global existence and singularity formation for a wave system modeling nematic liquid crystals in one space dimension. In our model, although the viscous damping term is included, the solution with smooth initial data still has gradient blowup in general, even when the initial energy is arbitrarily small. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：170 / 188

页数：19

共 19 条

[1] ORIENTATION WAVES IN A DIRECTOR FIELD WITH ROTATIONAL INERTIA [J].

Ali, Giuseppe ;

Hunter, John K. .

[2] Conservative solutions to a nonlinear variational wave equation [J].

Bressan, Alberto ;

Zheng, Yuxi .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 266 (02) :471-497

[3]

Chen Geng, 2012, COMM PURE A IN PRESS

[4] ON THE REGULARITY OF SPHERICALLY SYMMETRICAL WAVE MAPS [J].

CHRISTODOULOU, D ;

TAHVILDARZADEH, AS .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1993, 46 (07) :1041-1091

[5]

Coron J.-M., 1991, NEMATICS

[6]

Ericksen J. L., 1987, IMA VOLUMES MATH ITS, V5

[7] Singularities of a variational wave equation [J].

Glassey, RT ;

Hunter, JK ;

Zheng, YX .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 129 (01) :49-78

[8] EXISTENCE AND PARTIAL REGULARITY OF STATIC LIQUID-CRYSTAL CONFIGURATIONS [J].

HARDT, R ;

KINDERLEHRER, D ;

LIN, FH .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 105 (04) :547-570

[9]

Kinderlehrer D., 1991, FRONTIERS PURE APPL, P151

[10] COMPARISON-THEOREMS FOR DIFFERENTIAL-EQUATIONS [J].

MCNABB, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1986, 119 (1-2) :417-428

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