Line Defects in the Small Elastic Constant Limit of a Three-Dimensional Landau-de Gennes Model

详细信息    查看全文

• 作者：Giacomo Canevari
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：223
• 期：2
• 页码：591-676
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0673
• 卷排序：223

文摘

We consider the Landau-de Gennes variational model for nematic liquid crystals, in three-dimensional domains. More precisely, we study the asymptotic behaviour of minimizers as the elastic constant tends to zero, under the assumption that minimizers are uniformly bounded and their energy blows up as the logarithm of the elastic constant. We show that there exists a closed set \({\mathscr{S}_{\rm line}}\) of finite length, such that minimizers converge to a locally harmonic map away from \({\mathscr{S}_{\rm line}}\). Moreover, \({\mathscr{S}_{\rm line}}\) restricted to the interior of the domain is a locally finite union of straight line segments. We provide sufficient conditions, depending on the domain and the boundary data, under which our main results apply. We also discuss some examples.