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We investigate stability properties of the radially symmetric solutioncorresponding to the vortex defect (so called "melting hedgehog") in theframework of the Landau - de Gennes model of nematic liquid crystals. We provelocal stability of the melting hedgehog under arbitrary $Q$-tensor valuedperturbations in the temperature regime near the critical supercoolingtemperature. As a consequence of our method, we also rediscover the loss ofstability of the vortex defect in the deep nematic regime.

Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals