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Stability of half-degree point defect profiles for 2-D nematic liquid crystal

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      Abstract

      In this paper, we prove the stability of half-degree point defect profiles in \(\mathbb{R}^2\) for the nematic liquid crystal within Landau-de Gennes model.

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      The topological theory of defects in ordered media

       N. D. Mermin (1979)
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        Existence and partial regularity of static liquid crystal configurations

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          Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond

          We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in \(W^{1,2}\), to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions.
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            1601.02845

            Analysis

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