Instability of point defects 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

17 Citations (Scopus)
336 Downloads (Pure)


We study a class of symmetric critical points in a variational 2D Landau-de Gennes model where the state of nematic liquid crystals is described by symmetric traceless 3×3 matrices. These critical points play the role of topological point defects carrying a degree k/2 for a nonzero integer k. We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when |k|≥2.

Original languageEnglish
Pages (from-to)1131-1152
Number of pages22
JournalAnnales de l'Institut Henri Poincaré (C) Non Linear Analysis
Issue number4
Publication statusPublished - 16 Apr 2015


  • Liquid crystal defects
  • Nonlinear elliptic PDE system
  • Singular ODE system
  • Stability
  • Vortex


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