Global Weak Solutions for the Compressible Active Liquid Crystal System

TL;DR

This paper proves the existence of global weak solutions for the three-dimensional compressible active liquid crystal system using advanced mathematical techniques to handle active terms.

Contribution

It introduces new methods and estimates to establish global weak solutions for the complex active liquid crystal model.

Findings

Existence of global weak solutions in three dimensions.

Development of new analytical techniques for active terms.

Framework applicable to compressible active liquid crystal flows.

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.