Vector Field Models for Nematic Disclinations

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