On a hyperbolic system arising in liquid crystals modeling

被引：28
|
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.
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页码：15 / 35
页数：21
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