Communications in Mathematical Sciences

Volume 7 (2009)

Number 4

Vortices in two-dimensional nematics

Pages: 917 – 938



Ibrahim Fatkullin

Valeriy Slastikov


We study a two-dimensional model describing spatial variations of orientational ordering in nematic liquid crystals. In particular, we show that the spatially extended Onsager-Maier-Saupe free energy may be decomposed into Landau-de Gennes-type and relative entropy-type contributions. We then prove that in the high concentration limit the states of the system display characteristic vortex-like patterns and derive an asymptotic expansion for the free energy of the system.


Liquid crystals; nematics; spatial patterns; vortices

2010 Mathematics Subject Classification

82B21, 82B26, 82D30

Full Text (PDF format)