We use the framework of Landau-de Gennes theory to investigate various defect profiles and their stability in 2D and 3D liquid crystal systems. In 2D we show that a defect profile can be characterized by a system of ODEs. We show that in deep nematic regime this defect profile is a ground state of the liquid crystal system. In 3D we investigate the stability of radially symmetric profile ("melting hedgehog") corresponding to the point defect. We show its stability in the mathematically challenging temperature regime near the supercooling temperature.