# American Institute of Mathematical Sciences

April  2015, 8(2): 323-340. doi: 10.3934/dcdss.2015.8.323

## Diffusive transport in two-dimensional nematics

 1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, United States 2 Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

Received  June 2013 Revised  November 2013 Published  July 2014

We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational degrees of freedom. This diffusion induces a slow motion of singularities of the order parameter field. Using asymptotic methods for gradient flows, we establish a relation between the Doi-Smoluchowski kinetic equation and vortex dynamics in two-dimensional systems. We also discuss moment closures for the kinetic equation and Landau-de Gennes-type free energy dissipation.
Citation: Ibrahim Fatkullin, Valeriy Slastikov. Diffusive transport in two-dimensional nematics. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 323-340. doi: 10.3934/dcdss.2015.8.323
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##### References:
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