GLOBAL STRONG SOLUTIONS OF THE FULL NAVIER-STOKES AND Q-TENSOR SYSTEM FOR NEMATIC LIQUID CRYSTAL FLOWS IN TWO DIMENSIONS

被引：30

作者：

Cavaterra, Cecilia ^{[1
]}

Rocca, Elisabetta ^{[1
,2
]}

Wu, Hao ^{[3
,4
]}

Xu, Xiang ^{[5
]}

机构：

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Weierstr Inst Appl Anal & Stochast, D-10117 Berlin, Germany

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[4] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

[5] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 23529 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2016年 / 48卷 / 02期

关键词：

nematic liquid crystal flow; Q-tensor system; global strong solution; uniqueness of asymptotic limit; DE-GENNES THEORY; EVOLUTION-EQUATIONS; WELL-POSEDNESS; WEAK SOLUTIONS; EXISTENCE; REGULARITY; EQUILIBRIUM;

D O I：

10.1137/15M1048550

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter. that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate.

引用

页码：1368 / 1399

页数：32

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