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

Abstract

We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports independently of the number of Dirac Deltas in 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.

arXiv comment14 pages, 2 figures

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Cited by in corpus (12)

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• Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation
• Discrete minimisers are close to continuum minimisers for the interaction energy
• Pattern formation of a nonlocal, anisotropic interaction model
• Regularity of local minimizers of the interaction energy via obstacle problems
• Ground states of a two phase model with cross and self attractive interactions
• Asymptotic properties of short-range interaction functionals
• Minimizers of nonlocal interaction functional with exogenous potential
• Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
• Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials
• Convergence of regularized nonlocal interaction energies
• Particle approximation of nonlocal interaction energies