Abstract
In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [13]. Unlike previous results on the Cucker-Smale model, our approach is not based on the empirical measures, but, using an Eulerian point of view introduced in [9] in the Hamiltonian setting, we show the limit providing explicit constants. Moreover, for non strictly Cucker-Smale particles dynamics, we also give an insight on what induces a flocking behavior of the solution to the Vlasov equation to the - unknown a priori - flocking properties of the original particle system.
Anno
2022
Autori IAC
Tipo pubblicazione
Altri Autori
Natalini, Roberto; Paul, Thierry
Editore
Dept. of Mathematics, Southwest Missouri State University,
Rivista
Discrete and continuous dynamical systems. Series B