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

17 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

Fingerprint

Fluid Model
Kinetic Model
Hydrodynamic Limit
Alignment
Large Time Behavior
Fluid
Kinetics
Fluids
Averaging Lemmas
Hydrodynamics
Incompressible Navier-Stokes
Flocking
Lp Estimates
Navier-Stokes System
Existence of Weak Solutions
Relative Entropy
Energy Estimates
Coupled Model
Incompressible Navier-Stokes Equations
Classical Solution

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics

Cite this

@article{6071bfe52f264bbc9f3db4de1a35a522,
title = "On the analysis of a coupled kinetic-fluid model with local alignment forces",
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.",
author = "Carrillo, {Jose A.} and Choi, {Young Pil} and Karper, {Trygve K.}",
year = "2016",
month = "3",
day = "1",
doi = "10.1016/j.anihpc.2014.10.002",
language = "English",
volume = "33",
pages = "273--307",
journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",
issn = "0294-1449",
publisher = "Elsevier Masson SAS",
number = "2",

}

On the analysis of a coupled kinetic-fluid model with local alignment forces. / Carrillo, Jose A.; Choi, Young Pil; Karper, Trygve K.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 33, No. 2, 01.03.2016, p. 273-307.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the analysis of a coupled kinetic-fluid model with local alignment forces

AU - Carrillo, Jose A.

AU - Choi, Young Pil

AU - Karper, Trygve K.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84959295241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959295241&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2014.10.002

DO - 10.1016/j.anihpc.2014.10.002

M3 - Article

AN - SCOPUS:84959295241

VL - 33

SP - 273

EP - 307

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

SN - 0294-1449

IS - 2

ER -