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}
}
  • J. CarrilloRuiwen Shu
  • Published 11 July 2021
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
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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