Global Weak Solutions for the Compressible Active Liquid Crystal System

2017/11/14 by Gui‐Qiang Chen, Apala Majumdar, Chen, Gui-Qiang G. +5
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Micro and Nano Robotics #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.1711.04925

openalex publication_date 2017/11/14 · openalex created_date 2019/07/30 · openalex updated_date 2026/08/01

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.

Citations

• Some constitutive equations for liquid crystals
• The Physics of Liquid Crystals

Related

• Weak solutions to the equations of stationary compressible flows in active liquid crystals
• Global Existence and Regularity for the Active Liquid Crystal System
• Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals
• Global weak solution for a coupled compressible Navier-Stokes and Q-tensor system
• Existence of Global Weak Solutions to an Inhomogeneous Doi Model for Active Liquid Crystals