Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System

被引：91
|
作者：
Paicu, Marius [1 ]
Zarnescu, Arghir [2 ]
机构：
[1] Univ Bordeaux 1, IMB, F-33405 Talence, France
[2] Math Inst, Oxford OX1 3LB, England
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 203卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
NEMATIC LIQUID-CRYSTALS; FENE DUMBBELL MODEL; DE-GENNES THEORY; VISCOELASTIC FLUIDS; POLYMERIC FLOWS; WELL-POSEDNESS; EXISTENCE; EQUATIONS; HYDRODYNAMICS; ORDER;
D O I：
10.1007/s00205-011-0443-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a complex non-Newtonian fluid that models the flowof nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three.We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use cancellations that allow its existence to prove higher global regularity in dimension two. We also show the weak-strong uniqueness in dimension two.
引用
收藏
页码：45 / 67
页数：23
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