No. 2023.02
Vector Field Models for Nematic Disclinations
A. Acharya, I. Fonseca, L. Ganedi, and K. Stinson
Subject: Analysis of PDEs, materials science


In this paper, a model for defects that was introduced in \cite{ZANV} is studied. In the literature, the setting of most models for defects is the function space SBV (special bounded variation functions) (see, e.g., \cite{ContiGarroni, GoldmanSerfaty}). However, this model regularizes the director field to be in a Sobolev space by adding a second field to incorporate the defect. A relaxation result in the case of fixed parameters is proven along with some partial compactness results.