Time evolution of nematic liquid crystals with variable degree of orientation

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1033-1047
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume33
Issue number5
DOIs
StatePublished - 2002

Fingerprint

Nematic liquid crystals
Evolution System
Existence of Weak Solutions
Local Existence
Continuum Model
Nematic Liquid Crystal
Long-time Behavior
Behavior of Solutions
Classical Solution
Global Existence
Dissipation
Exact Solution

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Time evolution of nematic liquid crystals with variable degree of orientation. / Calderer, M. C.; Golovaty, D.; Lin, F. H.; Liu, C.

In: SIAM Journal on Mathematical Analysis, Vol. 33, No. 5, 2002, p. 1033-1047.

Research output: Contribution to journalArticle

Calderer, M. C. ; Golovaty, D. ; Lin, F. H. ; Liu, C. / Time evolution of nematic liquid crystals with variable degree of orientation. In: SIAM Journal on Mathematical Analysis. 2002 ; Vol. 33, No. 5. pp. 1033-1047.
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