From Particle to Kinetic and Hydrodynamic Descriptions of Flocking Seung-yeal Ha and Eitan Tadmor

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Abstract. 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.

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From Particle to Kinetic and Hydrodynamic Descriptions of Flocking

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تاریخ انتشار 2008