Eigenframe discontinuities of the Q-tensor model

Zhiyuan Geng; Changyou Wang

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arXiv · 2505.12179

Eigenframe discontinuities of the Q-tensor model

Zhiyuan Geng·Changyou Wang

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Abstract

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.

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Zhiyuan Geng, Changyou Wang. 2025-05-18. Eigenframe discontinuities of the Q-tensor model. https://arxiv.org/abs/2505.12179

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