Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids

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

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

We propose a coupled system for the interaction between Cucker-Smale ocking particles and viscous compressible fluids, and present a global existence theory and time-asymptotic behavior for the proposed model in the spatial periodic domain T3. Our model consists of the kinetic Cucker-Smale model for flocking particles and the isentropic compressible Navier-Stokes equations for fluids, and these two models are coupled through a drag force, which is responsible for the asymptotic alignment between particles and fluid. For the asymptotic flocking behavior, we explicitly construct a Lyapunov functional measuring the deviation from the asymptotic flocking states. For a large viscosity and small initial data, we show that the velocities of Cucker-Smale particles and fluids are asymptotically aligned to the common velocity.

Original languageEnglish
Pages (from-to)4419-4458
Number of pages40
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume34
Issue number11
DOIs
Publication statusPublished - 2014 Nov

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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