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<p>In this paper, we study the defect structure of minimizer of a Landau-de Gennes energy functional in three-dimensional domains, subject to constraint <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(|Q|=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>Q</mi> <mo stretchy="false">|</mo> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. 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 <i>Q</i>-tensor model.</p>

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Eigenframe discontinuities of the Q-tensor model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月10日

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  • Zhiyuan Geng,
  • Changyou Wang

摘要

In this paper, we study the defect structure of minimizer of a Landau-de Gennes energy functional in three-dimensional domains, subject to constraint \(|Q|=1\) | 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.