Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials

Kyungkeun Kang; Hwa Kil Kim; Tongseok Lim; Geuntaek Seo

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arXiv · 1907.07004

Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials

Kyungkeun Kang·Hwa Kil Kim·Tongseok Lim·Geuntaek Seo

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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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Kyungkeun Kang, Hwa Kil Kim, Tongseok Lim, Geuntaek Seo. 2019-07-16. Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials. https://arxiv.org/abs/1907.07004

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