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

Hyeong-Ohk Bae, Seung-Yeal Ha, Jeongho Kim, Dongnam Ko, Sung-Ik Sohn. Flocking Behaviors of a Cucker–Smale Ensemble in a Cylindrical Domain. SIAM J. Math. Anal., 51(3), pp. 2390–2424 (2019). DOI: https://doi.org/10.1137/18M122025X

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.

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