Singular alignment dynamics
数学专题报告
报告题目(Title)：Singular alignment dynamics
报告人(Speaker)： Jan Peszek (波兰 University of Warsaw)
地点(Place)：Zoom 会议 ID：951 888 04087, 密码：123456, Zoom Link: https://zoom.us/j/95188804087
时间(Time)：2024 年 4 月 19 日（周五） 16:00--17:00
邀请人(Inviter)：薛留堂
报告摘要
I will present the latest results and ideas related to the micro- to meso- and macroscopic limit for singular alignment dynamics. This includes the heterogeneous gradient flows related to weakly singular alignment (joint with David Poyato, University of Granada) with matrix valued communication, and a monokineticity property for kinetic strongly singular alignment (joint with Michał Fabisiak, University of Warsaw). In particular, I will show that any weakly continuous solution to strongly singular Cucker-Smale kinetic equation is monokinetic. This information can be used to obtain (via direct micro- to macroscopic mean-field limit) existence of measure-valued solutions to the fractional Euler-alignment system in the whole space for general initial data admitting vacuum.
