WEAK-STRONG UNIQUENESS FOR THE GENERAL ERICKSEN-LESLIE SYSTEM IN THREE DIMENSIONS

被引：6

作者：

Emmrich, Etienne ^{[1
]}

Lasarzik, Robert ^{[2
]}

机构：

[1] Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin, Germany

[2] Weierstrass Inst, Mohrenstr 39, D-10117 Berlin, Germany

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 09期

关键词：

Liquid crystal; Ericksen-Leslie equation; existence; weak solution; weak-strong uniqueness; NAVIER-STOKES EQUATIONS; COMPLETE FLUID SYSTEMS; LIQUID-CRYSTALS; RELATIVE ENTROPIES; THERMODYNAMICS; REGULARITY; EXISTENCE; FLOW;

D O I：

10.3934/dcds.2018202

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：4617 / 4635

页数：19

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