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 $\mathbb T^d$ and in an infinite channel.

Our coupled system consists of the kinetic Cucker-Smale 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 an individual C-S particle and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast.