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

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

4 Citations (Scopus)

163 Downloads (Pure)

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

Access to Document

10.1016/j.jde.2017.02.035

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

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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",

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AU - Chen, Gui Qiang

AU - Majumdar, Apala

AU - Wang, Dehua

AU - Zhang, Rongfang

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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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DO - 10.1016/j.jde.2017.02.035

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