GLOBAL WEAK SOLUTIONS FOR THE COMPRESSIBLE ACTIVE LIQUID CRYSTAL SYSTEM

被引：11

作者：

Chen, Gui-Qiang G. ^{[1
]}

Majumdar, Apala ^{[2
]}

Wang, Dehua ^{[3
]}

Zhang, Rongfang ^{[3
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 04期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

active hydrodynamics; active liquid crystals; compressible flows; Navier-Stokes equations; Q-tensor; global weak solutions; three-level approximations; weak convergence; GIANT NUMBER FLUCTUATIONS; NAVIER-STOKES; EXISTENCE; REGULARITY; EQUATIONS; DYNAMICS;

D O I：

10.1137/17M1156897

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the hydrodynamics of compressible flows of active liquid crystals in the Beris-Edwards hydrodynamics framework, using the Landau-de Gennes Q-tensor order parameter to describe liquid crystalline ordering. We prove the existence of global weak solutions for this active system in three space dimensions by the three-level approximations and weak convergence argument. New techniques and estimates are developed to overcome the difficulties caused by the active terms.

引用

页码：3632 / 3675

页数：44

共 57 条

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[Anonymous], 1994, An introduction to the mathematical theory of the Navier-Stokes equations

[2]

AUBIN JP, 1963, CR HEBD ACAD SCI, V256, P5042

[3] Orientability and Energy Minimization in Liquid Crystal Models [J].