cond-mat.soft

# Title:Nonstationary models for liquid crystals: A fresh mathematical perspective

Abstract: In this article we discuss nonstationary models for inhomogeneous liquid crystals driven out of equilibrium by flow. Emphasis is put on those models which are used in the mathematics as well as in the physics literature, the overall goal being to illustrate the mathematical progress on popular models which physicists often just solve numerically. Our discussion includes the Doi--Hess model for the orientational distribution function, the $Q$-tensor model and the Ericksen--Leslie model which focuses on the director dynamics. We survey particularly the mathematical issues (such as existence of solutions) and linkages between these models. Moreover, we introduce the new concept of relative energies measuring the distance between solutions of equation systems with nonconvex energy functionals and discuss possible applications of this concept for future studies.
 Subjects: Soft Condensed Matter (cond-mat.soft); Analysis of PDEs (math.AP) MSC classes: 76A15, 35Q35 DOI: 10.1016/j.jnnfm.2018.05.003 Cite as: arXiv:1708.06937 [cond-mat.soft] (or arXiv:1708.06937v1 [cond-mat.soft] for this version)

## Submission history

From: Robert Lasarzik [view email]
[v1] Wed, 23 Aug 2017 09:52:19 UTC (41 KB)
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