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

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 [dbl-struck T] super()d Our coupled system consists of the kinetic C-S equation and the incompressible Navier-Stokes equations, and...

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Bibliographic Details
Published in:Nonlinearity 2012-04, Vol.25 (4), p.1155-1177
Main Authors: BAE, Hyeong-Ohk, CHOI, Young-Pil, HA, Seung-Yeal, KANG, Moon-Jin
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Exact sciences and technology
Fluid flow
Fluids
Global analysis, analysis on manifolds
Incompressible flow
Joining
Mathematical analysis
Mathematical methods in physics
Mathematical models
Mathematics
Navier-Stokes equations
Other topics in mathematical methods in physics
Parametric inference
Partial differential equations
Physics
Probability and statistics
Sciences and techniques of general use
Statistics
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary: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 [dbl-struck T] super()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.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/25/4/1155