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On The Mean Field limit for Cucker-Smale models

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 [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.
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https://hal.archives-ouvertes.fr/hal-02008699
Contributor : Thierry Paul <>
Submitted on : Friday, February 5, 2021 - 7:44:26 AM
Last modification on : Wednesday, June 2, 2021 - 4:27:23 PM

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  • HAL Id : hal-02008699, version 5
  • ARXIV : 2011.12584

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Roberto Natalini, Thierry Paul. On The Mean Field limit for Cucker-Smale models. 2021. ⟨hal-02008699v5⟩

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