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Seung-Yeal Ha

2009-01-08
16:00:00 - 16:50:00

From particle to kinetic and fluid descriptions on flocking

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will present kinetic and fluid equations which can be formally derived from the Cucker-Smale system. I will also explain the formation of flokcing on the Cucker-Smale models based on the explicit construction of a Lyapunov functional. This result also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. For large particle systems, we give a rigorous justification for the mean-field limit from the many particle Cucker-Smale system to the Vlasov equation with flocking dissipation as the number of particles goes to infinity.