Complete classification of the asymptotical behavior for singular C-S Model on the real line
Xiongtao Zhang, Tingting Zhu · arXiv (Cornell University) · 2019
In this paper, we study the singular Cucker-Smale (C-S) model on the real line. For long range case, i.e. $β1$, we construct the uniform-in-time lower bound of the relative distance between particles and provide the sufficient and necessary condition for the emergence of multi-cluster formation. For critical case, i.e. $β=1$, we show the uniform lower bound of the relative distance and unconditional flocking emergence. These results provide a complete classification of the collective behavior for C-S model on the real line.