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

Applied Mathematics

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

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

Navier–Stokes equations
active liquid crystals
global well-posedness
weak solutions
strong solutions
weak-strong uniqueness

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10.1016/j.jde.2017.02.035

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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 = "Navier–Stokes equations, active liquid crystals, global well-posedness, weak solutions, strong solutions, weak-strong uniqueness",

author = "Gui-Qiang Chen 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 - Navier–Stokes equations

KW - active liquid crystals

KW - global well-posedness

KW - weak solutions

KW - strong solutions

KW - weak-strong uniqueness

U2 - 10.1016/j.jde.2017.02.035

DO - 10.1016/j.jde.2017.02.035

M3 - Article

SN - 0022-0396

VL - 263

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

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