Flocking Behaviors of a Cucker--Smale Ensemble in a Cylindrical Domain

Abstract

We study the Cucker--Smale (C-S) type model in a cylindrical domain with a specular reflection boundary condition. When there exist flocking forces along the normal direction to the boundary, then a “sticky wall" effect is numerically observed such that particles aggregate in a region near the wall of a cylinder. To avoid this sticky wall phenomenon, we adopt a flow-directional flocking force which has no force component normal to the boundary. As a result, we obtain the flocking behavior of particles along the flow direction. Moreover, the emergence of flocking also holds for the corresponding kinetic C-S model. We present a global existence of the classical solution to the kinetic C-S model with the specular reflection boundary condition. In addition, we perform numerical simulations for the particle and kinetic C-S models to demonstrate the aggregation behavior of flocking particles interacting with the boundary.