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A simple proof of the Cucker-Smale flocking dynamics and mean-field limit

Seung Yeal Ha Seoul National University Jian-Guo Liu Duke University

Analysis of PDEs mathscidoc:1702.03054

Communications in Mathematical Sciences, 7, (2), 297-325, 2009.4
We present a simple proof on the formation of flocking in the F. Cucker and S. Smale system [Jpn. J. Math. (3) 2, No. 1, 197–227 (2007; Zbl 1166.92323)] based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the initial states in which the exponential convergence to the flocking state will occur. For large particle systems, we give a rigorous justification for the mean-field limit from the many particle Cucker-Smale system to the Vlasov equation with flocking dissipation as the number of particles goes to infinity.
Flocking, swarming, emergence, self-driven particles system, autonomous agents, Vlasov equation, Lyapunov functional, measure valued solution, Kantorovich-Rubinstein distance.
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@inproceedings{seung2009a,
  title={A simple proof of the Cucker-Smale flocking dynamics and mean-field limit},
  author={Seung Yeal Ha, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209001042186083346},
  booktitle={Communications in Mathematical Sciences},
  volume={7},
  number={2},
  pages={297-325},
  year={2009},
}
Seung Yeal Ha, and Jian-Guo Liu. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. 2009. Vol. 7. In Communications in Mathematical Sciences. pp.297-325. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209001042186083346.
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