Global weak solutions for the compressive active liquid crystal system - Chen, G; Majumdar, A; Wang, D; Zhang, R (Society for Industrial and Applied Mathematics, 2018)
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.