2025/05/18 by Zhiyuan Geng, Geng, Zhiyuan, Changyou Wang +1
Mathematics · #35J50 #35J60 #58E20 #82D30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2505.12179
openalex publication_date 2025/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the defect structure of minimizer of a Landau-de Gennes energy functional in three-dimensional domains, subject to constraint |Q|=1. The set of defects is identified by discontinuities in both the eigenframe and the leading eigenvector. Through a blow-up analysis, we prove that the defect set is 1-rectifiable and classify the asymptotic profile of the leading eigenvector near singularities. This generalizes some previous results on the structure of ring disclinations in the Q-tensor model.