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

Seung-Yeal Ha, Jian-Guo Liu
2009 Communications in Mathematical Sciences  
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.
doi:10.4310/cms.2009.v7.n2.a2 fatcat:e7olxrwidnhtxbutjaril7pwly