From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials

José A. Carrillo; Ruiwen Shu

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arXiv · 2107.05079

From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials

José A. Carrillo·Ruiwen Shu

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Abstract

For the interaction energy with repulsive-attractive potentials, we give generic conditions which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein distance. As a consequence, we obtain the uniqueness of local minimizers in this topology for a class of interaction potentials. We introduce a novel notion of concavity of the interaction potential allowing us to show certain fractal-like behavior of the local minimizers. We provide a family of interaction potentials such that the support of the associated local minimizers has no isolated points and any superlevel set has no interior points.

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José A. Carrillo, Ruiwen Shu. 2021-07-11. From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials. https://arxiv.org/abs/2107.05079

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