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

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 a suitable concept of generalized gradient Young measures for this system. 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.