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Title: Some problems on the dynamics of nematic liquid crystals
Author: Wilkinson, Mark
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2013
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In this thesis, we consider two problems in the Q-tensor theory of nematic liquid crystals. The first concerns eigenvalue constraints on the Q-tensor order parameter. In particular, by employing a singular potential constructed by Ball and Majumdar, we consider the existence, regularity and "strict physicality" of weak solutions to the Beris-Edwards equations of nemato-hydrodynamics. In the second part of the thesis, we consider a gradient flow of the well-studied Landau-de Gennes energy. We prove some rigorous results on the average long-time statistical behaviour of its solutions, which are in agreement with experimental observations in the condensed matter physics literature.
Supervisor: Ball, John M.; Zarnescu, Arghir Sponsor: Engineering & Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics - Partial Differential Equations ; Partial Differential Equations - Liquid Crystals - Condensed Matter Physics