Monokineticity and mean-field limit for strongly singular Cucker-Smale model

Seminario de Jóvenes Investigadores

Speaker: Michał Fabisiak (University of Warsaw, Poland)

Abstract: Cucker-Smale model, introduced in 2007, describes the
evolution of particles alligning their velocities according to nonlocal
interaction protocol. We will focus on the strongly singular case and
see that, under some mild assumptions, measure valued solutions to
kinetic Cucker-Smale equations are in fact monokinetic, which reduces
them further to the hydrodynamic scale, known as Euler-alignment system.
Consequently, we are able to perform a direct micro- to macroscopic mean
field limit, proving the existence of weak solutions to one dimensional
Euler-alignent system with almost any initial data, including the
possibility of a vacuum. The talk is based on joint work with Jan Peszek
(University of Warsaw).