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June 2009 A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
Seung-Yeal Ha, Jian-Guo Liu
Commun. Math. Sci. 7(2): 297-325 (June 2009).

Abstract

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.

Citation

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Seung-Yeal Ha. Jian-Guo Liu. "A simple proof of the Cucker-Smale flocking dynamics and mean-field limit." Commun. Math. Sci. 7 (2) 297 - 325, June 2009.

Information

Published: June 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1177.92003
MathSciNet: MR2536440

Subjects:
Primary: 92C17
Secondary: 82C22 , 82C40

Keywords: autonomous agents , emergence , flocking , Kantorovich-Rubinstein distance , Lyapunov functional , measure valued solution , self-driven particles system , swarming , Vlasov equation

Rights: Copyright © 2009 International Press of Boston

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Vol.7 • No. 2 • June 2009
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