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Global well-posedness for Vlasov equations with power-law interactions in d≥4
Abstract
We study the Vlasov equation with general power-law (Riesz-type) potentials with exponent α. We prove global well-posedness in every dimension d≥4, for both attractive and repulsive interactions, throughout the range 0<α<3, for arbitrary nonnegative compactly supported bounded initial data. No smallness condition is imposed on the initial data. For the attractive problem, the virial identity gives finite-time breakdown for negative-energy solutions when α≥3. The proof of global well-posedness combines the analysis of characteristics, estimates in Lagrangian coordinates, and a crucial application of a \emph{compensated integrability} inequality due to Denis Serre.
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BibTeX
@misc{katriadakis2026global,
title = {{Global well-posedness for Vlasov equations with power-law interactions in $d\ge4$}},
author = {Emmanouil Katriadakis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09512},
eprint = {2609.09512},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09512},
}
RIS
TY - UNPB
TI - Global well-posedness for Vlasov equations with power-law interactions in d≥4
AU - Emmanouil Katriadakis
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09512
UR - https://arxiv.org/abs/2609.09512
AB - We study the Vlasov equation with general power-law (Riesz-type) potentials with exponent α. We prove global well-posedness in every dimension d≥4, for both attractive and repulsive interactions, throughout the range 0<α<3, for arbitrary nonnegative compactly supported bounded initial data. No smallness condition is imposed on the initial data. For the attractive problem, the virial identity gives finite-time breakdown for negative-energy solutions when α≥3. The proof of global well-posedness combines the analysis of characteristics, estimates in Lagrangian coordinates, and a crucial application of a \emph{compensated integrability} inequality due to Denis Serre.
ER -