Abstract
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.
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Communicated by F. Lin
Research supported by NSF grants FRG-DMS-0456286 and DMS-1109459.
Research supported by NSF grant FRG-DMS-0456286 and NRF of Korea Grant No. 2011-0014882.
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Bauman, P., Park, J. & Phillips, D. Analysis of Nematic Liquid Crystals with Disclination Lines. Arch Rational Mech Anal 205, 795–826 (2012). https://doi.org/10.1007/s00205-012-0530-7
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DOI: https://doi.org/10.1007/s00205-012-0530-7