WIAS Preprint No. 2966, (2022)

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


  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925
  • Reiter, Maximilian E. V.

2020 Mathematics Subject Classification

  • 35A35 35Q35 65M60 76A15


  • Existence, liquid crystal, Ericksen--Leslie, energy-variational solutions, numerical approximation, unit-norm constraint, mass-lumping, finite element method




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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