On the analysis of a coupled kinetic-fluid model with local alignment forces

Jose A. Carrillo, Young Pil Choi, Trygve K. Karper

Research output: Contribution to journalArticle

21 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)273-307
Number of pages35
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume33
Issue number2
DOIs
Publication statusPublished - 2016 Mar 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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