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

Abstract

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 $3\times 3$ 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 $k\ne \pm 1,0$.

References in corpus (2)

• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
• On the Disclination Lines of Nematic Liquid Crystals

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