Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

Radu Ignat*, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)
197 Downloads (Pure)

Abstract

We study k-radially symmetric solutions corresponding to topological defects of charge k2 for integer k≠ 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when | k| = 1 (unlike the case | k| > 1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.

Original languageEnglish
Article number119
Number of pages33
JournalCalculus of Variable and Partial Differential Equations
Volume55
Issue number5
Early online date23 Sep 2016
DOIs
Publication statusPublished - 1 Oct 2016

Keywords

  • 35A15
  • 35B38
  • 49J10
  • 49J30
  • 76A15
  • 82D30

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