Measure-valued solutions to the Ericksen--Leslie model equipped with the Oseen--Frank energy
- Lasarzik, Robert
2010 Mathematics Subject Classification
- 35Q35 35K65 76A15
- Liquid crystal, Ericksen-Leslie equation, existence, measure-valued solution, generalized Young measure
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.
- Nonlinear Analysis, 179 (2019), pp. 146--183 , DOI 10.1016/j.na.2018.08.013 .