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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.
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- 1 Finished
1/08/12 → 30/09/16
Project: Research council