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2021
- handle: 10670/1.7b4fgm
- hal: hal-02008699
- doi: 10.3934/dcdsb.2021164
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info:eu-repo/semantics/altIdentifier/doi/10.3934/dcdsb.2021164
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Roberto Natalini et al., « On The Mean Field limit for Cucker-Smale models », HAL-SHS : sociologie, ID : 10.3934/dcdsb.2021164
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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 [12].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 [8] in the Hamiltonian setting, we show the limit providing explicit constants.%Using an Eulerian point of view introduced in \cite{gmp} in the Hamiltonian setting, we don't use empirical measures and provide 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.