Abstract
In this paper, we are concerned with local minimizers of an interaction energy governed by repulsive–attractive potentials of power-law type in one dimension. We prove that sum of two Dirac masses is the unique local minimizer under the \(\lambda \)-Wasserstein metric topology with \(1\le \lambda <\infty \), provided masses and distance of Dirac deltas are equally half and one, respectively. In addition, in case of \(\infty \)-Wasserstein metric, we characterize stability of steady-state solutions depending on powers of interaction potentials.
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