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

详细信息    查看全文

• 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0294144915000402&_mathId=si1.gif&_user=111111111&_pii=S0294144915000402&_rdoc=1&_issn=02941449&md5=994ae24013a57673440e1c381a1b2ee3" title="Click to view the MathML source">3×3class="mathContainer hidden">class="mathCode">$3\times 3$ matrices. These critical points play the role of topological point defects carrying a degree class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0294144915000402&_mathId=si2.gif&_user=111111111&_pii=S0294144915000402&_rdoc=1&_issn=02941449&md5=c5034dea64c80be6a07e220c4954e6c2">class="imgLazyJSB inlineImage" height="21" width="9" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0294144915000402-si2.gif">class="mathContainer hidden">class="mathCode">$\frac{k}{2}$ 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0294144915000402&_mathId=si3.gif&_user=111111111&_pii=S0294144915000402&_rdoc=1&_issn=02941449&md5=dc175e8bcd9468cb9601e6bc02c12b5a" title="Click to view the MathML source">|k|≥2class="mathContainer hidden">class="mathCode">$|k|\ge 2$.