Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations
type: Item
instance of: scholarly article
title: Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations
zbMATH Open document ID: 1453.35141
author: Yunfei Su
author: Lei Yao
published in: Journal of Differential Equations
publication date: 2020-04-22T00:00:00Z
review text: The authors study the hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck (NS/VFP) equations in 2D or 3D bounded domains when the initial density is bounded away from zero. By employing the relative entropy techniques, the authors can first establish the strong convergence of the macroscopic density of particles in \(L^\infty (0, T; L^1(\Omega))\), and then they prove that weak solutions of the NS/VFP equations converge to the smooth solution of the limiting incompressible fluid model. Moreover, taking advantage of a compactness result for Orlicz spaces in 2D, the authors also obtain the hydrodynamic limit in the 2D case even when there is initial vacuum. The result of this paper extends the works of \textit{T. Goudon} et al. [Indiana Univ. Math. J. 53, No. 6, 1495--1515 (2004; Zbl 1085.35117)] and \textit{A. Mellet} and \textit{A. Vasseur} [Commun. Math. Phys. 281, No. 3, 573--596 (2008; Zbl 1155.35415)] to the inhomogeneous fluid case.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q84
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q83
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 7191470
zbMATH Keywords: hydrodynamic limit
zbMATH Keywords: inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations
zbMATH Keywords: relative entropy method
reviewed by: Song Jiang
MaRDI profile type: Publication
full work available at URL: j.jde.2019.12.027
OpenAlex ID: W2999418921
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DOI: 10.1016/J.JDE.2019.12.027
description: scientific article; zbMATH DE number 7191470