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

@article{Carrillo2021FromRS, title={From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials}, author={Jos{\'e} Antonio Carrillo and Ruiwen Shu}, journal={Calculus of Variations and Partial Differential Equations}, year={2021}, volume={62} }

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…

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