Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd(d=2,3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2:=R2/Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.