Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions
E Emmrich, R Lasarzik - arXiv preprint arXiv:1712.00660, 2017 - arxiv.org
E Emmrich, R Lasarzik
arXiv preprint arXiv:1712.00660, 2017•arxiv.orgWe 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 is that the relative energy inequality is proved for a system with a
nonconvex energy.
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 is that the relative energy inequality is proved for a system with a
nonconvex energy.
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 is that the relative energy inequality is proved for a system with a nonconvex energy.
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