On the mean field limit for Cucker-Smale models

<p style='text-indent:20px;'>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 [<xref ref-type="bibr" rid="b13">13</xref>]. 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 [<xref ref-type="bibr" rid="b9">9</xref>] 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.</p>