On a hyperbolic system arising in liquid crystals modeling

被引：30

作者：

Feireisl, Eduard ^{[1
]}

Rocca, Elisabetta ^{[2
]}

Schimperna, Giulio ^{[2
]}

Zarnescu, Arghir ^{[3
,4
,5
]}

机构：

[1] Acad Sci Czech Republ, Inst Math, Zitna 25, CZ-11567 Prague 1, Czech Republic

[2] Univ Pavia, Dipartimento Matemat, Via Ferrata 5, I-27100 Pavia, Italy

[3] Ikerbasque, Basque Fdn Sci, Maria Diaz de Haro 3, Bilbao 48013, Bizkaia, Spain

[4] BCAM, Basque Ctr Appl Math, Mazarredo 14, E-48009 Bilbao, Bizkaia, Spain

[5] Romanian Acad, Simion Stoilow Inst, 21 Calea Grivitei, Bucharest 010702, Romania

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2018年 / 15卷 / 01期

基金：

欧洲研究理事会;

关键词：

Liquid crystal; inviscid Qian-Sheng model; dissipative solution; weak-strong uniqueness; WEAK SOLUTIONS; EQUATIONS; FLOWS;

D O I：

10.1142/S0219891618500029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution is proposed, for which a global-in-time existence theorem is shown. The dissipative solutions enjoy the following properties: (i) they exist globally in time for any finite energy initial data; (ii) dissipative solutions enjoying certain smoothness are classical solutions; (iii) a dissipative solution coincides with a strong solution originating from the same initial data as long as the latter exists.

引用

页码：15 / 35

页数：21

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