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<p>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.</p>

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Formation of multiple flocks in a simple nonlocal aggregation model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月9日

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  • Carrie Clark

摘要

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.