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DDC: 510 × Subject: Ericksen-Leslie equation × Subject: Existence ×

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    Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions
    (Springfield, Mo. : American Institute of Mathematical Sciences, 2018) Emmrich, Etienne; Lasarzik, Robert
    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.