Time-asymptotic interaction of flocking particles and an incompressible viscous fluid

Hyeong Ohk Bae, Young Pil Choi, Seung Yeal Ha, Moon Jin Kang

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42 Citations (Scopus)

Abstract

We present a new coupled kinetic-fluid model for the interactions between CuckerSmale (C-S) flocking particles and incompressible fluid on the periodic spatial domain T d. Our coupled system consists of the kinetic C-S equation and the incompressible NavierStokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a global existence of weak solutions and a priori time-asymptotic exponential flocking estimates for any smooth flow, when the kinematic viscosity of the fluid is sufficiently large. The velocity of individual C-S particles and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast.

Original languageEnglish
Pages (from-to)1155-1177
Number of pages23
JournalNonlinearity
Volume25
Issue number4
DOIs
Publication statusPublished - 2012 Apr 1

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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