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arXiv · 1911.11258

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

Zhiyuan Geng·Wei Wang
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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 $\frac k2$ 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.

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Zhiyuan Geng, Wei Wang. 2019-11-25. Point defects in 2-D liquid crystals with singular potential: profiles and stability. https://arxiv.org/abs/1911.11258

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