From particle to kinetic and hydrodynamic descriptions of flocking
Seung-Yeal Ha - Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea (email)
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.
Keywords: flocking, particles, kinetic formulation, moments,
Received: June 2008; Revised: June 2008; Published: August 2008.
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