Collective Behavior: Macroscopic versus Kinetic Descriptions

Global classical solution and long time behavior of macroscopic flocking models

Changhui Tan

Rice University

Self-organized behaviors are very common in nature and human societies. One widely discussed example is the flocking phenomenon which discribes animal groups emerging towards the same direction. Several models such as Cucker-Smale and Motsch-Tadmor are very successful in characterizing flocking behaviors. In this talk, we will discuss macroscopic representation of flocking models. These systems can be interpreted as compressible Eulerian dynamics with nonlocal alignment forcing. We show global existence of classical solutions and long time flocking behavior of the system, when initial profile satisfies a threshold condition. On the other hand, another set of initial conditions will lead to a finite time break down of the system. This is a joint work with Eitan Tadmor.