On the analysis of a coupled kinetic-fluid model with local alignment forces
File(s)
Accepted version
Author(s)
Carrillo, JA
Choi, Y-P
Karper, TK
Type
Journal Article
Abstract
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier–Stokes equations. The model describes the motion of particles immersed in a Navier–Stokes fluid interacting through local alignment. We first prove the existence of weak solutions using energy and Lp estimates together with the velocity averaging lemma. We also rigorously establish a hydrodynamic limit corresponding to strong noise and local alignment. In this limit, the dynamics can be totally described by a coupled compressible Euler – incompressible Navier–Stokes system. The proof is via relative entropy techniques. Finally, we show a conditional result on the large-time behavior of classical solutions. Specifically, if the mass-density satisfies a uniform in time integrability estimate, then particles align with the fluid velocity exponentially fast without any further assumption on the viscosity of the fluid.
Date Issued
2014-10-22
Date Acceptance
2014-10-16
Citation
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2014, 33 (2), pp.273-307
ISSN
0294-1449
Publisher
Elsevier
Start Page
273
End Page
307
Journal / Book Title
Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Volume
33
Issue
2
Copyright Statement
© 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (E
Grant Number
EP/K008404/1
Subjects
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Notes
publisher: Elsevier articletitle: On the analysis of a coupled kinetic-fluid model with local alignment forces journaltitle: Annales de l'Institut Henri Poincare (C) Non Linear Analysis articlelink: http://dx.doi.org/10.1016/j.anihpc.2014.10.002 content_type: article copyright: Copyright © 2015 Elsevier Masson SAS. All rights reserved.
Publication Status
Published