Formation of multiple flocks in a simple nonlocal aggregation model

2021/10/16 by Clark, Carrie
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2110.08660

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 use the dichotomy case of the concentration compactness principle to obtain an energy minimizer, even though minimizing sequences are expected to break apart into flocks which may move far away from one another.

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