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We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b2 small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case b2 = 0, we investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.
- Liquid crystal defects
- Nonlinear elliptic PDE system
- Singular ODE system