Open AccessOn mathematical analysis of complex fluids in active hydrodynamics
Author(s) -
Yazhou Chen,
Dehua Wang,
Rongfang Zhang
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021063
Subject(s) - compressibility , uniqueness , compressible flow , tensor (intrinsic definition) , weak solution , physics , incompressible flow , mathematics , statistical physics , classical mechanics , mathematical analysis , mechanics , geometry
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.