On the Eulerian dynamics with nonlocal interactions
报告题目(Title)： On the Eulerian dynamics with nonlocal interactions
报告人(Speaker)：Tan Changhui （University of South Carolina）
地点(Place)：后主楼1223
时间(Time)：5月22日下午4:00-5:00
邀请人(Inviter)：薛留堂
报告摘要
The Euler-Alignment system arises as a macroscopic representation of the Cucker-Smale model, which describes the flocking phenomenon in animal swarms. The nonlinear and nonlocal nature of the system bring challenges in studying global regularity and long time behaviors. In this talk, I will discuss the global wellposedness of the Euler-Alignment system with three types of nonlocal alignment interactions: bounded, strongly singular, and weakly singular interactions. Different choices of interactions will lead to different global behaviors. I will also discuss interesting connections to some fluid dynamics systems, including the fractional Burgers equation, the porous medium equation, and the aggregation equation.
在这个报告中，我将向大家介绍欧拉-共向(Euler-Alignment)系统。这个系统是由Cucker-Smale模型推导出的宏观模型。它描述了自然界中常见的动物群聚现象。该系统中的非线性非局部的相互作用力对分析全局正则性和长时间行为产生了难度和挑战。我将讨论三种不同的共向作用力：有界的，强奇异的，和弱奇异的。不同的作用力会导致不同的全局行为。我还将讨论该系统与其它流体系统的联系，包括分数阶Burgers方程，多孔介质(porous medium)方程，以及聚合(aggregation)方程。
