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

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Date
2015-07-29MFO Scientific Program
Research in Pairs 2014Series
Oberwolfach Preprints;2015,05Author
Ignat, Radu
Nguyen, Luc
Slastikov, Valeriy
Zarnescu, Arghir
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Show full item recordOWP-2015-05
Abstract
We study a class of symmetric critical points in a variational 2$D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3 \times 3$ matrices. These critical points play the role of topological point defects carrying a degree $k\over 2$ 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 $|k| \geq 2$.