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Function Spaces for Liquid Crystals

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Abstract

We consider the relationship between three continuum liquid crystal theories: Oseen–Frank, Ericksen and Landau–de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function space choices for the order parameters s, n, and Q, we establish connections between the variational formulations of these theories. We use these results to justify a version of the Oseen–Frank theory using special functions of bounded variation. This proposed model can describe both orientable and non-orientable defects. Finally we study a number of frustrated nematic and cholesteric liquid crystal systems and show that the model predicts the existence of point and surface discontinuities in the director.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

    Stephen Bedford

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  1. Stephen Bedford
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Correspondence to Stephen Bedford.

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Communicated by A. Braides

This work was supported by the EPSRC Science and Innovation award to the Oxford Centre for Nonlinear PDE (EP/E035027/1). The author is supported by CASE studentship with Hewlett-Packard Limited.

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Bedford, S. Function Spaces for Liquid Crystals. Arch Rational Mech Anal 219, 937–984 (2016). https://doi.org/10.1007/s00205-015-0913-7

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