Instability of point defects in a two-dimensional nematic liquid crystal model

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• 作者：Radu Ignat^a ; ^{Radu.Ignat@math.univ-toulouse.fr" class="auth_mail" title="E-mail the corresponding author} ; Luc Nguyen^b ; ^{luc.nguyen@maths.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Valeriy Slastikov^c ; ^{Valeriy.Slastikov@bristol.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Arghir Zarnescu^d ; ^e ; ^{A.Zarnescu@sussex.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlinear elliptic PDE system ; Singular ODE system ; Stability ; Vortex ; Liquid crystal defects
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2016
• 出版时间：July-August 2016
• 年：2016
• 卷：33
• 期：4
• 页码：1131-1152
• 全文大小：463 K

文摘

We study a class of symmetric critical points in a variational 2D   Landau–de Gennes model where the state of nematic liquid crystals is described by symmetric traceless 3×3$3\times 3$ matrices. These critical points play the role of topological point defects carrying a degree $\frac{k}{2}$ for a nonzero integer k  . We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when |k|≥2$|k|\ge 2$.