We study k-radially symmetric solutions corresponding to topological defects of charge k2 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.
|Number of pages||33|
|Journal||Calculus of Variable and Partial Differential Equations|
|Early online date||23 Sep 2016|
|Publication status||Published - 1 Oct 2016|