| Contents |
| We propose a coupled system for the interaction between Cucker-Smale
flocking particles and viscous compressible fluids, and present a
global existence theory and time-asymptotic behavior for the
proposed model in the spatial periodic domain. 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. |
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