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 language | English |
|---|---|
| Pages (from-to) | 273-307 |
| Number of pages | 35 |
| Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
| Volume | 33 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2016 Mar 1 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Mathematical Physics
- Applied Mathematics
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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 journal › Article
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 -