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

Ha, Seung-Yeal; Liu, Jian-Guo

Commun. Math. Sci., Tome 7 (2009) no. 1, p. 297-325 / Harvested from Project Euclid

Résumé

We present a simple proof on the formation of flocking to the Cucker-Smale system 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 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.

Publié le : 2009-06-15
Classification: Flocking, swarming, emergence, self-driven particles system, autonomous agents, Vlasov equation, Lyapunov functional, measure valued solution, Kantorovich-Rubinstein distance, 92C17, 82C22, 82C40

@article{1243443982,
     author = {Ha, Seung-Yeal and Liu, Jian-Guo},
     title = {A simple proof of the Cucker-Smale flocking dynamics and mean-field limit},
     journal = {Commun. Math. Sci.},
     volume = {7},
     number = {1},
     year = {2009},
     pages = { 297-325},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1243443982}
}

Ha, Seung-Yeal; Liu, Jian-Guo. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. Commun. Math. Sci., Tome 7 (2009) no. 1, pp.  297-325. http://gdmltest.u-ga.fr/item/1243443982/