Blowup Rate Estimates of a Singular Potential and Its Gradient in the Landau-de Gennes Theory
Blowup Rate Estimates of a Singular Potential and Its Gradient in the Landau-de Gennes Theory
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DOI：
10.1007/s00332-021-09761-x
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发表时间：
2021-11
影响因子：
3
通讯作者：
X. Lu;Xiang Xu;Wujun Zhang
中科院分区：
文献类型：
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作者：
X. Lu;Xiang Xu;Wujun Zhang
在这篇论文中，我们重新审视了一个奇异体势的Landau-de Gennes自由能，它描述了液晶组态的Q-张量序参量的框架。这种Maier-Saupe型奇异势最初在Katriel等人（Mol Cryst Liquid Cryst 1：337-355，1986）中引入，其被认为是对对称、无痕Q张量的本征值的物理约束的自然强制。具体地说，我们建立了这个奇异的潜力和它的梯度爆破率作为Q接近其物理边界。所有的证明都是基本的。
In this paper, we revisit a singular bulk potential in the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the framework of theQ-tensor order parameter. This Maier–Saupe type singular potential was originally introduced in Katriel et al. (Mol Cryst Liquid Cryst 1:337–355, 1986), which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, tracelessQ-tensors. Specifically, we establish blowup rates of both this singular potential and its gradient asQapproaches its physical boundary. All of the proofs are elementary.