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.

References in corpus (12)

• Spontaneous motion in hierarchically assembled active matter
• Large-scale collective properties of self-propelled rods
• Defect annihilation and proliferation in active nematics
• Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Fluctuations and Pattern Formation in Self-Propelled Particles
• Biphasic, Lyotropic, Active Nematics
• Excitable Patterns in Active Nematics
• Banding, Excitability and Chaos in Active Nematic Suspensions
• Active nematics are intrinsically phase-separated
• Well-posedness of the Ericksen-Leslie system
• The small Deborah number limit of the Doi-Onsager equation to the Ericksen-Leslie equation