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.
Original language | English |
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Pages (from-to) | 3632–3675 |
Number of pages | 44 |
Journal | SIAM Journal on Mathematical Analysis (SIMA) |
Volume | 50 |
Issue number | 4 |
DOIs | |
Publication status | Published - 10 Jul 2018 |
Keywords
- active hydrodynamics
- weak convergence
- three-level approximations
- global weak solutions
- $Q$-tensor
- Navier--Stokes equations
- compressible flows
- active liquid crystals