Point defects in 2-D liquid crystals with singular potential: profiles and stability

Abstract

We study radial symmetric point defects with degree $\frac{k}{2}$ in 2D disk or ${\mathbb{R}}^2$ in $Q$-tensor framework with singular bulk energy, which is defined by Bingham closure. First, we obtain the existence of solutions for the profiles of radial symmetric point defects with degree $\frac{k}{2}$ in 2D disk or ${\mathbb{R}}^2$. Then we prove that the solution is stable for $|k|=1$ and unstable for $|k|>1$. Some identities are derived and used throughout the proof of existence and stability/instability.

References in corpus (6)

• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
• On Minimizers of the Landau-de Gennes Energy Functional on Planar Domains
• Half-integer point defects in the $Q$-tensor theory of nematic liquid crystals
• Instability of point defects in a two-dimensional nematic liquid crystal model
• Some properties of the nematic radial hedgehog in Landau-de Gennes' theory
• Regularity of Minimizers of a Tensor-valued Variational Obstacle Problem in Three Dimensions