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

2016/01/12 by Radu Ignat, Luc Nguyen, Ignat, Radu +5
Materials Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Liquid Crystal Research Advancements #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.1601.02812

openalex publication_date 2016/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study k-radially symmetric solutions corresponding to topological defects of charge (k)/(2) 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.

Citations

• Existence of solitary waves in higher dimensions
• The Physics of Liquid Crystals

Related

• Stability of half-degree point defect profiles for 2-D nematic liquid crystal
• Liquid crystal defects in the Landau-de Gennes theory in two dimensions-beyond the one-constant approximation
• Point defects in 2-D liquid crystals with singular potential: profiles and stability
• Nematic equilibria on a two-dimensional annulus: defects and energies
• Transition of defect patterns from 2D to 3D in liquid crystals