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Analysis of nematic liquid crystals with disclination lines. (English) Zbl 1281.76020
Summary: We investigate the structure of nematic liquid crystal thin films described by the Landau-de Gennes tensor-valued order parameter model with Dirichlet boundary conditions on the sides of nonzero degree. We prove that as the elasticity constant goes to zero in the energy, a limiting uniaxial nematic texture forms with a finite number of defects, all of degree \({\frac{1}{2}}\) or all of degree \(-\frac{1}{2}\), corresponding to vertical disclination lines at those locations. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.

MSC:
76A15 Liquid crystals
35Q35 PDEs in connection with fluid mechanics
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