Global weak solutions for the compressible active liquid crystal system

Gui Qiang G. Chen, Apala Majumdar, Dehua Wang, Rongfang Zhang

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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.
Original languageEnglish
Pages (from-to)3632–3675
Number of pages44
JournalSIAM Journal on Mathematical Analysis (SIMA)
Issue number4
Publication statusPublished - 10 Jul 2018


  • active hydrodynamics
  • weak convergence
  • three-level approximations
  • global weak solutions
  • $Q$-tensor
  • Navier--Stokes equations
  • compressible flows
  • active liquid crystals


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