Formation of multiple flocks in a simple nonlocal aggregation model

Abstract We consider a family of interaction energies given by kernels having a “well-barrier" shape, and investigate how these kernels drive the formation of multiple flocks within a larger population. We show that the energy is minimized by a sequence of indicators of finitely many balls whose supports become infinitely far apart from one another. The dichotomy case of the concentration compactness principle is a key ingredient in our proof.