LAUSR

Abstract 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 R d ( d = 2 , 3 ) . Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R 2 . In a large coupling regime and periodic spatial domain T 2 : = R 2 / Z 2 , we show that the velocities of C–S particles and fluids are asymptotically aligned to two constant velocities which may be different.