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

被引：94

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

页码：45 / 67

页数：23

共 29 条

[1]

[Anonymous], 1998, Perfect Incompressible Fluids

[2] Existence of global weak solutions for some polymeric flow models [J].