title: On global minimizers of repulsive-attractive power-law interaction energies.
abstract: 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.
authors.affiliation: Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, UK carrillo@imperial.ac.uk.
authors.forename: José Antonio
authors.initials: JA
authors.lastname: Carrillo
authors.affiliation: Institut für Mathematik, Angewandte Mathematik, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
authors.forename: Michel
authors.initials: M
authors.lastname: Chipot
authors.affiliation: Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, UK.
authors.forename: Yanghong
authors.initials: Y
authors.lastname: Huang
keywords: global discrete minimizers; interaction energy; swarming models