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Publication 14-CNA-018

Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals

Gautam Iyer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
gautam@math.cmu.edu

Xiang Xu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh PA 15213-3890 USA
xuxiang@andrew.cmu.edu

Arghir Zarnescu
Department of Mathematics
University of Sussex
Pevensey III, Falmer, BN1 9QH, United Kingdom
A.Zarnescu@sussex.ac.uk

Abstract: We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal congurations described using the Q-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical effects produced by the presence of this cubic term by considering an L2 gradient flow generated by this energy. We work in two dimensions and concentrate on understanding the relations between the physicality of the initial data and the global well-posedness of the system.

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