Weak-strong uniqueness for the general Ericksen—Leslie system in three dimensions

Etienne Emmrich; Robert Lasarzik

doi:10.3934/dcds.2018202

Article Contents

2018, Volume 38, Issue 9: 4617-4635. Doi: 10.3934/dcds.2018202 open access

This issue Previous Article Moving planes for nonlinear fractional Laplacian equation with negative powers Next Article Local well-posedness and blow-up criteria of magneto-viscoelastic flows

Weak-strong uniqueness for the general Ericksen—Leslie system in three dimensions

Etienne Emmrich^1, , and
Robert Lasarzik^2,

1.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
2.
Weierstrass Institute, Mohrenstraße 39, 10117 Berlin, Germany

* Corresponding author
* Corresponding author

Received: November 2017

Revised: April 2018

Published: September 2018

This work was funded by CRC 901 Control of self-organizing nonlinear systems: Theoretical methods and concepts of application (Project A8)

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Abstract

We study the Ericksen-Leslie system equipped with a quadratic free energy functional. The norm restriction of the director is incorporated by a standard relaxation technique using a double-well potential. We use the relative energy concept, often applied in the context of compressible Euler- or related systems of fluid dynamics, to prove weak-strong uniqueness of solutions. A main novelty, not only in the context of the Ericksen-Leslie model, is that the relative energy inequality is proved for a system with a nonconvex energy.

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Mathematics Subject Classification: Primary: 35Q35, 35D30; Secondary: 35K52, 76A15.

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