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 reection boundary condition. When there exist ocking 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 ow-directional ocking force which has no force component normal to the boundary. As a result, we obtain the ocking behavior of particles along the ow direction. Moreover, the emergence of ocking 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 reection boundary condition. In addition, we perform numerical simulations for the particle and kinetic C-S models to demonstrate the aggregation behavior of ocking particles interacting with the boundary.