2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

Critical thresholds on compressible Euler dynamics with nonlocal viscosity

Changhui Tan

University of Maryland

We study the macroscopic representation of Cucker-Smale and other related flocking systems. As a hydrodynamic limit of the kinetic model, the system acts like compressible Euler equations with nonlocal viscosity. Taking advantage of the non-locality and flocking properties, we prove global regularity of the system under suitable initial configuration determined by an upper critical threshold of the initial data. A lower critical threshold can also be generated which leads to a finite time blowup. This is a joint work with Professor Eitan Tadmor.