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We discuss the Cucker-Smale's (C-S) particle model for flocking, derivingprecise conditions for flocking to occur when pairwise interactions aresufficiently strong long range. We then derive a Vlasov-type kinetic model forthe C-S particle model and prove it exhibits time-asymptotic flocking behaviorfor arbitrary compactly supported initial data. Finally, we introduce ahydrodynamic description of flocking based on the C-S Vlasov-type kinetic modeland prove flocking behavior \emph{without} closure of higher moments.

From particle to kinetic and hydrodynamic descriptions of flocking