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

Cucker-Smale model, introduced in 2007, describes the evolution of particles aligning 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 the Euler-alignment 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) and Young-Pil Choi (Yonsei University).