On the Interactions of Flocking Particles with the Stokes Flow in an Infinite Channel

Abstract

We present the global existence of weak solutions to the Cucker–Smale–Stokes system in an infinitely long cylindrical domain with the specular boundary condition. The proposed system consists of the kinetic Cucker–Smale model and the Stokes system for flocking particles and an incompressible fluid, respectively, in an infinitely long cylindrical domain. It models the collective dynamics resulting from the fluid-particle-structure interactions. For this model, we provide the global existence of a weak solution and numerical simulations that exhibit collective behaviors of flocking particles.