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

Abstract

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

References in corpus (5)

• Introduction to Q-tensor theory
• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
• Minimizers of the Landau-de Gennes energy around a spherical colloid particle
• Dimension reduction for the Landau-de Gennes model on curved nematic thin films
• On the Disclination Lines of Nematic Liquid Crystals