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

Speaker(s)

Michał Fabisiak

Affiliation

doktorant SDNŚiS

Date

April 13, 2023, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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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)

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