Global weak solutions for the compressible active liquid crystal system

Gui Qiang G. Chen; Apala Majumdar; Dehua Wang; Rongfang Zhang

doi:10.1137/17M1156897

Global weak solutions for the compressible active liquid crystal system

Gui Qiang G. Chen, Apala Majumdar, Dehua Wang, Rongfang Zhang

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	3632-3675
Number of pages	44
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	4
DOIs	https://doi.org/10.1137/17M1156897
Publication status	Published - 10 Jul 2018

Keywords

active hydrodynamics
weak convergence
three-level approximations
global weak solutions
$Q$-tensor
Navier--Stokes equations
compressible flows
active liquid crystals

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10.1137/17M1156897

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title = "Global weak solutions for the compressible active liquid crystal system",

abstract = "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.",

keywords = "active hydrodynamics, weak convergence, three-level approximations, global weak solutions, \$Q\$-tensor, Navier--Stokes equations, compressible flows, active liquid crystals",

author = "Chen, \{Gui Qiang G.\} and Apala Majumdar and Dehua Wang and Rongfang Zhang",

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T1 - Global weak solutions for the compressible active liquid crystal system

AU - Chen, Gui Qiang G.

AU - Majumdar, Apala

AU - Wang, Dehua

AU - Zhang, Rongfang

PY - 2018/7/10

Y1 - 2018/7/10

N2 - 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.

AB - 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.

KW - active hydrodynamics

KW - weak convergence

KW - three-level approximations

KW - global weak solutions

KW - $Q$-tensor

KW - Navier--Stokes equations

KW - compressible flows

KW - active liquid crystals

UR - https://www.scopus.com/pages/publications/85055283074

U2 - 10.1137/17M1156897

DO - 10.1137/17M1156897

M3 - Article

SN - 1095-7154

VL - 50

SP - 3632

EP - 3675

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

Global weak solutions for the compressible active liquid crystal system

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Keywords

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