Measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank energy
arXiv:1711.04638 · doi:10.1016/j.na.2018.08.013
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.
arXiv admin note: text overlap with arXiv:1711.03371
References in corpus (4)
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Cited by in corpus (12)
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- Nonstationary models for liquid crystals: A fresh mathematical perspective
- Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy
- Well-posedness of the Ericksen-Leslie System for the Oseen-Frank Model in L^3_{uloc}(\mathbb{R}^3)
- Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system
- Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
- Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models
- Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions
- Convergence of the Ginzburg-Landau approximation for the Ericksen-Leslie system
- Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations
- Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations