Eigenframe discontinuities of the Q-tensor model
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908369203232768 |
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| author | Geng, Zhiyuan Wang, Changyou |
| author_facet | Geng, Zhiyuan Wang, Changyou |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenframe discontinuities of the Q-tensor model Geng, Zhiyuan Wang, Changyou Analysis of PDEs 35J50, 35J60, 58E20, 82D30 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. |
| title | Eigenframe discontinuities of the Q-tensor model |
| topic | Analysis of PDEs 35J50, 35J60, 58E20, 82D30 |
| url | https://arxiv.org/abs/2505.12179 |