Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Multi-scale representations of flocking models and critical thresholds for the hydrodynamics

Changhui Tan

University of Maryland

Self-organized behavior is very common in nature and human societies. One widely discussed example is the flock formed by birds flying towards the same direction. Several models such as Cucker-Smale and Motsch-Tadmor are very successful in characterizing the flocking behavior. In this talk, we will discuss the flocking models in different scales, describing the alignment phenomenon. In particular, the hydrodynamic representation of the flocking models yields a very interesting fluid system: compressible Eulerian dynamics with nonlocal alignment. We show a critical threshold phenomenon for the fluid system. Under suitable initial conditions, the system has global strong solution, and it converges to a flock. 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.