Limiting configurations for solutions to the 1D Euler Alignment System
数学专题报告
报告题目(Title)：Limiting configurations for solutions to the 1D Euler Alignment System
报告人(Speaker)：Trevor Leslie (Illinois Institute of Technology, USA)
地点(Place)：Zoom 会议 ID：824 090 54803 , 密码：123456, Zoom Link: https://us02web.zoom.us/j/82409054803
时间(Time)：2024 年 10 月 23 日（周三） 10:00--11:00
邀请人(Inviter)：薛留堂
报告摘要
The Euler Alignment system is a hydrodynamic PDE version of the celebrated Cucker-Smale ODE's of collective behavior. Together with Changhui Tan (University of South Carolina), we developed a theory of weak solutions in 1D, which provides a uniquely determined way to evolve the dynamics after a blowup. Inspired by Brenier and Grenier's work on the pressureless Euler equations, we show that the dynamics of interest are captured by a nonlocal scalar balance law, the unique entropy solution of which we generate through a discretization involving the "sticky particle Cucker-Smale" system. In this talk, we will discuss the formation of clusters of mass in the Euler Alignment system, and we will describe how to predict these clusters using the flux from the associated scalar balance law.
