Description:
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 3x3 matrices. These critical points play the role of topological point defects carrying a degree 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| >2.