From kinetic to fluid models of liquid crystals by the moment method
Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo (2022), From kinetic to fluid models of liquid crystals by the moment method, Kinetic & Related Models, 15, 3, p. 417-465. 10.3934/krm.2021047
TypeArticle accepté pour publication ou publié
Journal nameKinetic & Related Models
AIMS - American Institute of Mathematical Sciences
MetadataShow full item record
Institut de Mathématiques de Toulouse UMR5219 [IMT]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)This paper deals with the convergence of the Doi-Navier-Stokes model of liquid crystals to the Ericksen-Leslie model in the limit of the Deborah number tending to zero. While the literature has investigated this problem by means of the Hilbert expansion method, we develop the moment method, i.e. a method that exploits conservation relations obeyed by the collision operator. These are non-classical conservation relations which are associated with a new concept, that of Generalized Collision Invariant (GCI). In this paper, we develop the GCI concept and relate it to geometrical and analytical structures of the collision operator. Then, the derivation of the limit model using the GCI is performed in an arbitrary number of spatial dimensions and with non-constant and non-uniform polymer density. This non-uniformity generates new terms in the Ericksen-Leslie model.
Subjects / KeywordsDoi equation; Maier-Saupe interaction; Q-tenso; Deborah number; Ericksen-Leslie equations; Oseen-Franck energy; order parameter; generalized collision invariant
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