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

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We present a new coupled kinetic-fluid model for the interactions between Cucker-Smale (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 Navier-Stokes 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.
Publisher
IOP PUBLISHING LTD
Issue Date
2012-04
Language
English
Article Type
Article
Citation

NONLINEARITY, v.25, no.4

ISSN
0951-7715
DOI
10.1088/0951-7715/25/4/1155
URI
http://hdl.handle.net/10203/278736
Appears in Collection
MA-Journal Papers(저널논문)
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