Young Researchers Workshop: Kinetic descriptions in theory and applications

On the Euler-Alignment system

Changhui Tan

University of South Carolina

The Euler-Alignment system arises as a macroscopic representation of the Cucker-Smale model, which describes the flocking phenomenon in animal swarms. The system is derived by Ha and Tadmor, through a kinetic description. The nonlocal interaction and the nonlinear 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, and the aggregation equation.