From particle to kinetic and hydrodynamic descriptions of flocking
From particle to kinetic and hydrodynamic descriptions of flocking
复制标题
DOI：
10.3934/krm.2008.1.415
复制
发表时间：
2008-06
影响因子：
1
通讯作者：
Seung‐Yeal Ha;E. Tadmor
中科院分区：
文献类型：
--
作者：
Seung‐Yeal Ha;E. Tadmor
我们讨论了植绒的 Cucker-Smale (C-S) 粒子模型，推导出当成对相互作用足够强的长程时发生植绒的精确条件。然后，我们推导出 C-S 粒子模型的 Vlasov 型动力学模型，并证明它对于任意紧支持的初始数据表现出时间渐近聚集行为。最后，我们介绍了基于 C-S Vlasov 型动力学模型的植绒流体动力学描述，并证明了无需高矩闭合的植绒行为。
We discuss the Cucker-Smale's (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S particle model and prove it exhibits time-asymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynamic description of flocking based on the C-S Vlasov-type kinetic model and prove flocking behavior without closure of higher moments.