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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.
|Number of pages||22|
|Journal||Annales de l'Institut Henri Poincaré (C) Non Linear Analysis|
|Publication status||Published - 16 Apr 2015|
- Liquid crystal defects
- Nonlinear elliptic PDE system
- Singular ODE system