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

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 3×33×3 matrices. These critical points play the role of topological point defects carrying a degree k2 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|≥2|k|≥2.