二维液晶模型中$\pm \frac 1 2$度点缺陷的稳定性
Stability of point defects of degree $\pm \frac 1 2$ in a two-dimensional nematic liquid crystal model
摘要：
研究了二维液晶的Landau-de Gennes模型中整数$k \neq 0$的电荷$\frac{k}{2}$拓扑缺陷对应的$k$ -径向对称解.我们表明，解决方案的径向轮廓满足自然符号不变性是稳定的，当$|k| = 1$（不像情况$|k|>1$，我们之前处理）。证明关键使用的单调性的适当的组件，通过利用系统的合作性质。还建立了径向轮廓的唯一性结果。
英文摘要：
We study $k$-radially symmetric solutions corresponding to topological defects of charge $\frac{k}{2}$ for integer $k \neq 0$ in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when $|k| = 1$ (unlike the case $|k|>1$ which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.
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