On global minimizers of repulsive-attractive power-law interaction energies

José Antonio Carrillo, Michel Chipot, Yanghong Huang

    Research output: Contribution to journalArticlepeer-review


    We consider the minimization of the repulsive–attractive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations.

    Original languageEnglish
    Article number20130399
    JournalPhilos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
    Issue number2028
    Publication statusPublished - 13 Nov 2014


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