| Abstract: |
| We present a coupled kinetic-fluid model for the interaction between Cucker-Smale(C-S) flocking particles and incompressible fluid. We consider the interaction behavior on the periodic spatial domain, and in the infinite channel with specular boundary condition.
Our coupled system consists of the kinetic C-S equation and the Navier-Stokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a existence of weak solutions and a time-asymptotic
exponential flocking estimates for smooth flow. The velocity of an individual C-S particles and fluid velocity tend to the averaged
time-dependent particle velocities exponentially fast.
We also provide numerical simulations. From them we observe the interaction behaves like non-Newtonian shear thinning flow. |
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