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

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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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  • 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.

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


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