WIAS Preprint No. 2476, (2018)

Measure-valued solutions to the Ericksen--Leslie model equipped with the Oseen--Frank energy



Authors

  • Lasarzik, Robert

2010 Mathematics Subject Classification

  • 35Q35 35K65 76A15

Keywords

  • Liquid crystal, Ericksen-Leslie equation, existence, measure-valued solution, generalized Young measure

DOI

10.20347/WIAS.PREPRINT.2476

Abstract

In this article, we prove the existence of measure-valued solutions to the Ericksen-Leslie system equipped with the Oseen--Frank energy. We introduce the concept of generalized gradient Young measures. Via a Galerkin approximation, we show the existence of weak solutions to a regularized system and attain measure-valued solutions for vanishing regularization. Additionally, it is shown that the measure-valued solution fulfills an energy inequality.

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