Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy
Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy
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具有次二次弹性能的 Landau-de Gennes 能量的极小化
DOI：
10.1007/s00205-019-01376-7
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发表时间：
2019
影响因子：
2.5
通讯作者：
Canevari G
中科院分区：
文献类型：
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作者：
Canevari G
我们研究了一种修正的向列液晶的Landau-de Gennes模型，其中弹性项在梯度中被假设为次二次增长。我们分析了全局最小值在二维和三维域中的行为，服从单轴边界条件，在渐近状态下，缺陷核的长度尺度比区域的长度尺度小。我们得到了最小值及其梯度的一致收敛性，远离极限单轴映射的奇异点。当温度足够低时，我们还证明了在二维域的最小化器中存在最大双轴核。
We study a modified Landau–de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains, subject to uniaxial boundary conditions, in the asymptotic regime where the length scale of the defect cores is small compared to the length scale of the domain. We obtain uniform convergence of the minimizers and of their gradients, away from the singularities of the limiting uniaxial map. We also demonstrate the presence of maximally biaxial cores in minimizers on two-dimensional domains, when the temperature is sufficiently low.