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arXiv · 1711.04638

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

Robert Lasarzik
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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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Robert Lasarzik. 2017-11-13. Measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank energy. https://doi.org/10.1016/j.na.2018.08.013

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