Nonstationary models for liquid crystals: A fresh mathematical perspective
arXiv:1708.06937 · doi:10.1016/j.jnnfm.2018.05.003
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 -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.
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Cited by in corpus (7)
- Maximal dissipative solutions for incompressible fluid dynamics
- Weak-strong uniqueness for measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank free energy
- Measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank energy
- Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy
- Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system
- Existence of weak solutions to the Ericksen-Leslie model for a general class of free energies
- Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations