Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

Existence of regular solutions to an Ericksen–Leslie model of the liquid crystal system

Pages: 1711 – 1740



Mimi Dai (Department of Applied Mathematics, University of Colorado, Boulder, Colo., U.S.A.)


We study a general Ericksen–Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi’s relation. We prove that in two dimension, the solutions are globally regular with general data, and in three dimension, the solutions are globally regular with small initial data or for a short time with large data. Moreover, a weak-strong type of uniqueness result is obtained.


liquid crystals, Parodi’s relation, regularity

2010 Mathematics Subject Classification


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