Open AccessOn the mean field limit for Cucker-Smale models
Author(s) -
Roberto Natalini,
Thierry Paul
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021164
Subject(s) - flocking (texture) , mathematics , limit (mathematics) , eulerian path , a priori and a posteriori , mathematical physics , mathematical analysis , statistical physics , physics , lagrangian , quantum mechanics , philosophy , epistemology
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.