Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations
Numerical Analysis
2023-12-22 v1 Numerical Analysis
Analysis of PDEs
Abstract
We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain choice of the regularity weight, the existence of energy-variational solutions implies the existence of measure-valued solutions and for a different choice, we construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm.
Keywords
Cite
@article{arxiv.2210.17242,
title = {Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations},
author = {Robert Lasarzik and Maximilian E. V. Reiter},
journal= {arXiv preprint arXiv:2210.17242},
year = {2023}
}