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

2013/11/21 by José A. Carrillo, Carrillo, J. A., Young-Pil Choi +3 · 4 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1311.5584

openalex publication_date 2013/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L^p 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.

Citations

• The second law of thermodynamics and stability

Cited by

• Relaxation limit and asymptotic stability for the Euler-Navier-Stokes equations
• Hydrodynamic limit for compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force
• Coupled Vlasov and non-Newtonian fluid dynamics: existence and large-time behavior
• Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force

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