Global existence and regularity of solutions for active liquid crystals

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

doi:10.1016/j.jde.2017.02.035

Global existence and regularity of solutions for active liquid crystals

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

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Abstract

We study the hydrodynamics of active liquid crystals in the Beris-Edwards hydrodynamic framework with the Landau-de Gennes Q-tensor order parameter to describe liquid crystalline ordering. The existence of global weak solutions in two and three spatial dimensions is established. In the two-dimensional case, by the Littlewood-Paley decomposition, the higher regularity of the weak solutions and the weak-strong uniqueness are also obtained.

Original language	English
Pages (from-to)	202-239
Number of pages	38
Journal	Journal of Differential Equations
Volume	263
Issue number	1
Early online date	3 Mar 2017
DOIs	https://doi.org/10.1016/j.jde.2017.02.035
Publication status	Published - 5 Jul 2017

Keywords

Active liquid crystals
Global well-posedness
Navier-Stokes equations
Strong solutions
Weak solutions
Weak-strong uniqueness

ASJC Scopus subject areas

Analysis

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10.1016/j.jde.2017.02.035

Accepted VersionAccepted author manuscript, 376 KBLicence: CC BY-NC-ND

https://arxiv.org/abs/1509.02608

Cite this

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title = "Global existence and regularity of solutions for active liquid crystals",

abstract = "We study the hydrodynamics of active liquid crystals in the Beris-Edwards hydrodynamic framework with the Landau-de Gennes Q-tensor order parameter to describe liquid crystalline ordering. The existence of global weak solutions in two and three spatial dimensions is established. In the two-dimensional case, by the Littlewood-Paley decomposition, the higher regularity of the weak solutions and the weak-strong uniqueness are also obtained.",

keywords = "Active liquid crystals, Global well-posedness, Navier-Stokes equations, Strong solutions, Weak solutions, Weak-strong uniqueness",

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

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T1 - Global existence and regularity of solutions for active liquid crystals

AU - Chen, Gui Qiang

AU - Majumdar, Apala

AU - Wang, Dehua

AU - Zhang, Rongfang

PY - 2017/7/5

Y1 - 2017/7/5

N2 - We study the hydrodynamics of active liquid crystals in the Beris-Edwards hydrodynamic framework with the Landau-de Gennes Q-tensor order parameter to describe liquid crystalline ordering. The existence of global weak solutions in two and three spatial dimensions is established. In the two-dimensional case, by the Littlewood-Paley decomposition, the higher regularity of the weak solutions and the weak-strong uniqueness are also obtained.

AB - We study the hydrodynamics of active liquid crystals in the Beris-Edwards hydrodynamic framework with the Landau-de Gennes Q-tensor order parameter to describe liquid crystalline ordering. The existence of global weak solutions in two and three spatial dimensions is established. In the two-dimensional case, by the Littlewood-Paley decomposition, the higher regularity of the weak solutions and the weak-strong uniqueness are also obtained.

KW - Active liquid crystals

KW - Global well-posedness

KW - Navier-Stokes equations

KW - Strong solutions

KW - Weak solutions

KW - Weak-strong uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85014210348&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2017.02.035

DO - 10.1016/j.jde.2017.02.035

M3 - Article

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VL - 263

SP - 202

EP - 239

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -

Global existence and regularity of solutions for active liquid crystals

Abstract

Keywords

ASJC Scopus subject areas

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