论文标题
在Cucker-Smale型号的平均场上限制上
On The Mean Field limit for Cucker-Smale models
论文作者
论文摘要
在本说明中，我们考虑了cucker-smale动力系统的概括，我们在瓦斯施泰因类型的拓扑中严格得出了对弗拉索夫型方程的平均场景极限（和混乱的繁殖）[12]中引入的vlasov-type方程。哈密顿设置，我们使用\ cite {gmp}中引入的欧拉观点（GMP}中引入的欧拉观点提供了明确的常数。％，我们不使用经验措施并提供明确的常数。此外，对于非严格的cucker -smale颗粒动力学，我们还深入了解了诱导溶液对vlasov方程的植入行为，以对原始粒子系统的 - 未知的先验蜂群。
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.
