Stability of point defects of degree ± 1 2 in a two-dimensional nematic liquid crystal model

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We study k-radially symmetric solutions corresponding to topological defects of charge k/2 for integer k ≠ 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when |k| = 1 (unlike the case |k|>1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.