Instability of point defects in a two-dimensional nematic liquid crystal model

Abstract

We study a class of symmetric critical points in a variational 2 D Landau–de Gennes model where the state of nematic liquid crystals is described by symmetric traceless 3 \times 3 matrices. These critical points play the role of topological point defects carrying a degree \frac{k}{2} 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| \geq 2 .