Abstract
We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (so called "melting hedgehog") in the framework of the Landau - de Gennes model of nematic liquid crystals. We prove local stability of the melting hedgehog under arbitrary $Q$-tensor valued perturbations in the temperature regime near the critical supercooling temperature. As a consequence of our method, we also rediscover the loss of stability of the vortex defect in the deep nematic regime.
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