Hydrodynamic limits of a Vlasov-Fokker-Planck equation for granular media
type: Item
instance of: scholarly article
title: Hydrodynamic limits of a Vlasov-Fokker-Planck equation for granular media
zbMATH Open document ID: 1087.82020
author: Dario Benedetto
author: Emanuele Caglioti
author: François Golse
author: Mario Pulvirenti
published in: Communications in Mathematical Sciences
publication date: 2006-02-08T00:00:00Z
review text: The authors consider the two types of scaling of the Vlasov equation for the phase space density \(f\) with Fokker-Planck term [VFP eq.]. Using the solutions of the zeroth order equations in these scalings, resp., they linearize the mean-field operator which appears in the VFP eq. It is shown that the resulting linearized operators satisfy the Fredholm alternative. This allows to perform the Hilbert or Chapman-Enskog expansions for the solutions of VFP eq. in these scalings. The zeroth and the first order terms of these expansions give the corrections to the conservation law for the macroscopic density and the bulk velocity which are defined by the integrals of the phase space density \(f\).
reviewed by: Hiroshi Tamura
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 76T25
Mathematics Subject Classification ID: 76M45
zbMATH DE Number: 5004818
zbMATH Keywords: Granular media
zbMATH Keywords: Vlasov-Fokker-Planck equation
zbMATH Keywords: Hydrodynamic limit
zbMATH Keywords: Hilbert expansion, Chapman-Enskog expansion
MaRDI profile type: Publication
DOI: 10.4310/CMS.2004.V2.N1.A7
description: scientific article; zbMATH DE number 5004818