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From kinetic to fluid models of liquid crystals by the moment method

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03275272
Contributor : Pierre Degond Connect in order to contact the contributor
Submitted on : Thursday, August 4, 2022 - 4:13:09 PM
Last modification on : Saturday, August 6, 2022 - 3:53:17 AM

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  • HAL Id : hal-03275272, version 2

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Pierre Degond, Amic Frouvelle, Jian-Guo Liu. From kinetic to fluid models of liquid crystals by the moment method. Kinetic and Related Models , AIMS, 2022, 15, pp.417-465. ⟨hal-03275272v2⟩

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