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",

year = "2017",

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journal = "Journal of Differential Equations",

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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

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U2 - 10.1016/j.jde.2017.02.035

DO - 10.1016/j.jde.2017.02.035

M3 - Article

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SN - 0022-0396

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SP - 202

EP - 239

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Global existence and regularity of solutions for active liquid crystals

Abstract

Keywords

ASJC Scopus subject areas

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Fellowship - The Mathematics of Liquid Crystals: Analysis, Computation and Applications

Cite this

Global existence and regularity of solutions for active liquid crystals

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Fellowship - The Mathematics of Liquid Crystals: Analysis, Computation and Applications

Cite this