Global weak solutions for the compressible active liquid crystal system

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)3632–3675
Number of pages44
JournalSIAM Journal on Mathematical Analysis (SIMA)
Volume50
Issue number4
DOIs
Publication statusPublished - 10 Jul 2018

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Global Weak Solutions
Liquid Crystal
Hydrodynamics
Compressible Flow
Weak Convergence
Order Parameter
Tensor
Liquid
Term
Approximation
Estimate
Framework

Keywords

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

Cite this

Chen, G. Q. G., Majumdar, A., Wang, D., & Zhang, R. (2018). Global weak solutions for the compressible active liquid crystal system. SIAM Journal on Mathematical Analysis (SIMA), 50(4), 3632–3675. https://doi.org/10.1137/17M1156897
Chen, Gui Qiang G. ; Majumdar, Apala ; Wang, Dehua ; Zhang, Rongfang. / Global weak solutions for the compressible active liquid crystal system. In: SIAM Journal on Mathematical Analysis (SIMA). 2018 ; Vol. 50, No. 4. pp. 3632–3675.
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Chen, GQG, Majumdar, A, Wang, D & Zhang, R 2018, 'Global weak solutions for the compressible active liquid crystal system', SIAM Journal on Mathematical Analysis (SIMA), vol. 50, no. 4, pp. 3632–3675. https://doi.org/10.1137/17M1156897

Global weak solutions for the compressible active liquid crystal system. / Chen, Gui Qiang G.; Majumdar, Apala; Wang, Dehua; Zhang, Rongfang.

In: SIAM Journal on Mathematical Analysis (SIMA), Vol. 50, No. 4, 10.07.2018, p. 3632–3675.

Research output: Contribution to journalArticle

TY - JOUR

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

U2 - 10.1137/17M1156897

DO - 10.1137/17M1156897

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SP - 3632

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Chen GQG, Majumdar A, Wang D, Zhang R. Global weak solutions for the compressible active liquid crystal system. SIAM Journal on Mathematical Analysis (SIMA). 2018 Jul 10;50(4):3632–3675. https://doi.org/10.1137/17M1156897