Global weak solutions for the compressible active liquid crystal system

Chen, Gui Qiang G. and Majumdar, Apala and Wang, Dehua and Zhang, Rongfang (2018) Global weak solutions for the compressible active liquid crystal system. SIAM Journal on Mathematical Analysis (SIMA), 50 (4). 3632–3675.

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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.