Vector Field Models for Nematic Disclinations

Journal of Nonlinear Science, vol. 33

Abstract

Abstract In this paper, a model for defects in nematic liquid crystals that was introduced in Zhang et al. (Physica D Nonlinear Phenom 417:132828, 2021) is studied. In the literature, the setting of many models for defects is the function space SBV (special functions of bounded variation). However, the model considered herein regularizes the director field to be in a Sobolev space by introducing a second vector field tracking the defect. A relaxation result in the case of fixed parameters is proved along with some partial compactness results as the defect width vanishes.

Authors 4

1. Amit Acharya

   Carnegie Mellon University

   Affiliation as printed

   Department of Civil and Environmental Engineering and Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

2. Irene Fonseca

   Carnegie Mellon University

   Affiliation as printed

   Department of Mathematics and Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

3. Likhit Ganedi Aachen Institut für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Mathematik RWTH Aachen, Templergraben 55, 52062, Aachen, Germany

4. Kerrek Stinson corresponding

   University of Bonn · Hausdorff Center for Mathematics

   Affiliation as printed

   Hausdorff Center for Mathematics, University of Bonn, Endenicher Allee 62, 53115, Bonn, Germany