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

Abstract

We study radial symmetric point defects with degree k 2 in 2D disk or 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 k 2 in 2D disk or 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.