Young Researchers Workshop: Kinetic models in biology and social sciences

On the hydrodynamic limit of Vlasov-type equations in a regime of strong local alignment

Moon-Jin Kang

Sookmyung Women's University

In this talk, I will mainly handle the kinetic Cucker-Smale model with local alignment as a mesoscopic description for the flocking dynamics. The local alignment was first proposed by Karper, Mellet and Trivisa, as a singular limit of a normalized non-symmetric alignment introduced by Motsch and Tadmor. I will present a proof for the rigorous justification on the hydrodynamic limit of the kinetic Cucker-Smale model with local alignment towards the pressureless Euler system with nonlocal alignment, in a regime of strong local alignment. If time permits, I will briefly give you another result on the hydrodynamic limit of the Vlasov-Poisson system with the local alignment.