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Preservation and Loss of Log-Concavity in the Repulsive Vlasov--Poisson System
Abstract
Prékopa's theorem shows that, for jointly log-concave initial data, free transport preserves the log-concavity of spatial densities. This paper asks whether this property persists in the repulsive Vlasov--Poisson system. In dimensions two and higher, we construct smooth, strongly log-concave initial distributions whose spatial densities lose log-concavity at arbitrarily small positive times. For one-dimensional cold-ion data, we prove that the spatial density remains log-concave for all time.
Related
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BibTeX
@misc{sun2026preservation,
title = {{Preservation and Loss of Log-Concavity in the Repulsive Vlasov--Poisson System}},
author = {Xiaoxiao Sun and Zhaopeng Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07380},
eprint = {2611.07380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07380},
}
RIS
TY - UNPB
TI - Preservation and Loss of Log-Concavity in the Repulsive Vlasov--Poisson System
AU - Xiaoxiao Sun
AU - Zhaopeng Wang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07380
UR - https://arxiv.org/abs/2611.07380
AB - Prékopa's theorem shows that, for jointly log-concave initial data, free transport preserves the log-concavity of spatial densities. This paper asks whether this property persists in the repulsive Vlasov--Poisson system. In dimensions two and higher, we construct smooth, strongly log-concave initial distributions whose spatial densities lose log-concavity at arbitrarily small positive times. For one-dimensional cold-ion data, we prove that the spatial density remains log-concave for all time.
ER -