Pedro Acevez Sanchez: Hydrodynamic limits for kinetic flocking models of Cucker-Smale type

Speaker
Pedro Acevez Sanchez, University of Arizona 

Abstract
In this talk, we analyze the asymptotic behavior for kinetic models describing the collective behavior of agents. We focus on models for self-propelled individuals whose velocity relaxes towards the mean orientation of their neighbors. The self-propulsion and friction forces, together with the orientation and noise, are interpreted as a collision/interaction mechanism acting with equal strength. We show that the set of “generalized collision invariants” in our setting is equivalent to the more classical notion of collision invariants, i.e., the kernel of a suitably linearized collision operator. After identifying these collision invariants, we derive the fluid model by appealing to the balances for particle concentration and orientation. We conclude this talk by investigating the main properties of the macroscopic model for a general potential with radial symmetry.