Global Weak Solutions for the Compressible Active Liquid Crystal System

Apala Majumdar

doi:10.1137/17M1156897

Global Weak Solutions for the Compressible Active Liquid Crystal System

Apala Majumdar

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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 language	English
Pages (from-to)	3632–3675
Journal	SIAM Journal on Mathematical Analysis (SIMA)
Volume	50
Issue number	4
Early online date	10 Jul 2018
DOIs	https://doi.org/10.1137/17M1156897
Publication status	Published - 2018

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10.1137/17M1156897

SIMA_2018_zhang_wang_chen_majumdar
The final publication is © SIAM and available at SIAM journals via https://doi.org/10.1137/17M1156897.
Accepted author manuscript, 433 KB

https://arxiv.org/abs/1711.04925

Fellowship - The Mathematics of Liquid Crystals: Analysis, Computation and Applications
Majumdar, A. (PI)
Engineering and Physical Sciences Research Council
1/08/12 → 30/09/16
Project: Research council

Cite this

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title = "Global Weak Solutions for the Compressible Active Liquid Crystal System",

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.",

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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.

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DO - 10.1137/17M1156897

M3 - Article

SN - 0036-1410

VL - 50

SP - 3632

EP - 3675

JO - SIAM Journal on Mathematical Analysis (SIMA)

JF - SIAM Journal on Mathematical Analysis (SIMA)

IS - 4

ER -

Global Weak Solutions for the Compressible Active Liquid Crystal System

Abstract

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Projects

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

Cite this