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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2016

Stability of point defects of degree $\pm \frac 1 2$ in a two-dimensional nematic liquid crystal model

Radu Ignat
Valeriy Slastikov
  • Fonction : Auteur
Arghir Zarnescu
  • Fonction : Auteur

Résumé

We study $k$-radially symmetric solutions corresponding to topological defects of charge $\frac{k}{2}$ for integer $k \neq 0$ 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.

Dates et versions

hal-01673404 , version 1 (29-12-2017)

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Citer

Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu. Stability of point defects of degree $\pm \frac 1 2$ in a two-dimensional nematic liquid crystal model. Calculus of Variations and Partial Differential Equations, 2016, ⟨10.1007/s00526-016-1051-2⟩. ⟨hal-01673404⟩
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