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.
\u2217Received by the editors October 11, 2018; accepted for publication (in revised form) April 9, 2019; published electronically June 6, 2019. http://www.siam.org/journals/sima/51-3/M122025.html Funding: The work of the first author was supported by NRF grant NRF-2018R1D1A1A09082848. The work of the second author was supported by the Samsung Science and Technology Foundation under project SSTF-BA1401-03. The work of the third author was supported by the German Research Foundation (DFG) under project IRTG 2235. The work of the fourth author was supported by the European Research Council under European Unions Horizon 2020 Research and Innovation Programme grant ERC-2015-AdG-694126-DyCon and by CNCS-UEFISCDI grant PN-III-P4-ID-PCE-2016-0035. The work of the fifth author was supported by NRF grant NRF-2018R1A2B6002164.
