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 λ-Wasserstein metric topology with 1 ≤ λ< ∞, provided masses and distance of Dirac deltas are equally half and one, respectively. In addition, in case of ∞-Wasserstein metric, we characterize stability of steady-state solutions depending on powers of interaction potentials.
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2021 Feb|
Bibliographical notePublisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
All Science Journal Classification (ASJC) codes
- Applied Mathematics