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

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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.
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Issue Date
2014-11
Language
English
Article Type
Article
Citation

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.34, no.11, pp.4419 - 4458

ISSN
1078-0947
DOI
10.3934/dcds.2014.34.4419
URI
http://hdl.handle.net/10203/279842
Appears in Collection
MA-Journal Papers(저널논문)
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