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On global minimizers of repulsive-attractive power-law interaction energies
José Antonio Carrillo1, Michel Chipot2, Yanghong Huang3
1Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, UK carrillo@imperial.ac.uk.
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.
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