2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

Existence of weak solutions and hydrodynamic limit of kinetic flocking models

Trygve Karper

University of Maryland

In this talk, we will consider the kinetic Cucker-Smale model with additional local alignment. For this model we will first prove the existence of weak solutions. Then, we will consider rigorously the flow regime where noise and local alignment are relatively large compared to the other effects. Our main result will be that the evolution can be totally described by a compressible Euler type system for the mass density and momentum. Tools involved in the analysis are the velocity averaging lemma and relative entropy.