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arXiv · 2210.17242

Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations

Robert Lasarzik·Maximilian E. V. Reiter
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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.

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Robert Lasarzik, Maximilian E. V. Reiter. 2022-10-31. Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations. https://doi.org/10.1007/s10440-023-00563-9

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