We consider a variational two-dimensional Landau–de Gennes model in the theory of nematic liquid crystals in a disk of radius R . We prove that under a symmetric boundary condition carrying a topological defect of degree $$\frac{k}{2}$$ k 2 for some given even non-zero integer k , there are exactly two minimizers for all large enough R . We show that the minimizers do not inherit the full symmetry structure of the energy functional and the boundary data. We further show that there are at least five symmetric critical points.

中文翻译：

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液晶二维朗道-德热内斯模型中解的对称性和多重性

我们在半径为 R 的圆盘中考虑向列液晶理论中的变分二维朗道-德热内斯模型。我们证明，在对称边界条件下，对于某些给定的非零整数 k ，在带有度数 $$\frac{k}{2}$$k 2 的拓扑缺陷下，对于所有足够大的 R ，恰好有两个极小值。我们表明最小化器没有继承能量泛函和边界数据的完全对称结构。我们进一步表明至少有五个对称临界点。