Time evolution of nematic liquid crystals with variable degree of orientation

M. C. Calderer; D. Golovaty; F. H. Lin; C. Liu

doi:10.1137/S0036141099362086

Time evolution of nematic liquid crystals with variable degree of orientation

M. C. Calderer, D. Golovaty, F. H. Lin, C. Liu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an evolution system, describing the time-dependent behavior of nematic liquid crystals with variable degree of orientation within the continuum model of Ericksen. We establish a dissipation relation and prove both the global existence of weak solutions and the local existence of classical solutions. Furthermore, we investigate the stability and long-time behavior of solutions and obtain an exact solution of the corresponding stationary system in a one-dimensional case.

Original language	English (US)
Pages (from-to)	1033-1047
Number of pages	15
Journal	SIAM Journal on Mathematical Analysis
Volume	33
Issue number	5
DOIs	https://doi.org/10.1137/S0036141099362086
State	Published - 2002

Keywords

Free energy functional
Nematic liquid crystals
Reaction-diffusion mechanism
Weak solutions

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036141099362086

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T1 - Time evolution of nematic liquid crystals with variable degree of orientation

AU - Calderer, M. C.

AU - Golovaty, D.

AU - Lin, F. H.

AU - Liu, C.

PY - 2002

Y1 - 2002

N2 - We consider an evolution system, describing the time-dependent behavior of nematic liquid crystals with variable degree of orientation within the continuum model of Ericksen. We establish a dissipation relation and prove both the global existence of weak solutions and the local existence of classical solutions. Furthermore, we investigate the stability and long-time behavior of solutions and obtain an exact solution of the corresponding stationary system in a one-dimensional case.

AB - We consider an evolution system, describing the time-dependent behavior of nematic liquid crystals with variable degree of orientation within the continuum model of Ericksen. We establish a dissipation relation and prove both the global existence of weak solutions and the local existence of classical solutions. Furthermore, we investigate the stability and long-time behavior of solutions and obtain an exact solution of the corresponding stationary system in a one-dimensional case.

KW - Free energy functional

KW - Nematic liquid crystals

KW - Reaction-diffusion mechanism

KW - Weak solutions

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -

Time evolution of nematic liquid crystals with variable degree of orientation

Abstract

Keywords

ASJC Scopus subject areas

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