We study a class of symmetric critical points in a variational 2D Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless 3×3 matrices. These critical points play the role of topological point defects carrying a degree 2k for a nonzero integer k. We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when k=±1,0.
@article{arxiv.1503.03670,
title = {Instability of point defects in a two-dimensional nematic liquid crystal model},
author = {Radu Ignat and Luc Nguyen and Valeriy Slastikov and Arghir Zarnescu},
journal= {arXiv preprint arXiv:1503.03670},
year = {2016}
}