On mathematical analysis of complex fluids in active hydrodynamics

Yazhou Chen; Dehua Wang; Rongfang Zhang; Yazhou Chen; Dehua Wang; Rongfang Zhang

doi:10.3934/era.2021063

Electronic Research Archive

2021, Volume 29, Issue 6: 3817-3832. doi: 10.3934/era.2021063

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On mathematical analysis of complex fluids in active hydrodynamics

Yazhou Chen ^{1
,},
Dehua Wang ^{2
,
,},
Rongfang Zhang ^{2
,}

1.
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
2.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received: 01 May 2021 Revised: 01 June 2021 Published: 13 August 2021
Primary: 35Q35, 76D05; Secondary: 76A15

This is a survey article for this special issue providing a review of the recent results in the mathematical analysis of active hydrodynamics. Both the incompressible and compressible models are discussed for the active liquid crystals in the Landau-de Gennes Q-tensor framework. The mathematical results on the weak solutions, regularity, and weak-strong uniqueness are presented for the incompressible flows. The global existence of weak solution to the compressible flows is recalled. Other related results on the inhomogeneous flows, incompressible limits, and stochastic analysis are also reviewed.
- Active liquid crystals,
- active hydrodynamics,
- Q-tensor,
- global weak solutions,
- regularity,
- weak-strong uniqueness,
- incompressible limit
Citation: Yazhou Chen, Dehua Wang, Rongfang Zhang. On mathematical analysis of complex fluids in active hydrodynamics[J]. Electronic Research Archive, 2021, 29(6): 3817-3832. doi: 10.3934/era.2021063

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Abstract

This is a survey article for this special issue providing a review of the recent results in the mathematical analysis of active hydrodynamics. Both the incompressible and compressible models are discussed for the active liquid crystals in the Landau-de Gennes Q-tensor framework. The mathematical results on the weak solutions, regularity, and weak-strong uniqueness are presented for the incompressible flows. The global existence of weak solution to the compressible flows is recalled. Other related results on the inhomogeneous flows, incompressible limits, and stochastic analysis are also reviewed.

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