Global classical solutions of the repulsive relativistic Vlasov--Poisson system
Abstract
Global classical existence for general large data in the three-dimensional repulsive relativistic Vlasov--Poisson system has long been an open problem. We give an affirmative answer: every nonnegative C1 initial datum satisfying f0(x,p)+|∇x,pf0(x,p)|≲⟨ x⟩−a⟨ p⟩−b, a>1, b>3, generates a unique global classical solution. No smallness or symmetry is assumed. The result covers finite and infinite mass and energy, including infinite kinetic energy density. The power thresholds are sharp for general pure-power bounds ensuring finite density and an absolutely convergent Coulomb field. The proof rests on two new mechanisms: local energy recovery for a population selected by energy growth, and a corrected moment--action closure based on nonnegative transverse interactions. The argument also yields global classical solutions of the nonrelativistic equation in the same initial class, allowing infinite mass with polynomial velocity tails of any order b>3.
Related
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BibTeX
@misc{huang2026global,
title = {{Global classical solutions of the repulsive relativistic Vlasov--Poisson system}},
author = {Feimin Huang and Jingpeng Wu and Hang Xiong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01004},
eprint = {2611.01004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01004},
}
RIS
TY - UNPB
TI - Global classical solutions of the repulsive relativistic Vlasov--Poisson system
AU - Feimin Huang
AU - Jingpeng Wu
AU - Hang Xiong
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01004
UR - https://arxiv.org/abs/2611.01004
AB - Global classical existence for general large data in the three-dimensional repulsive relativistic Vlasov--Poisson system has long been an open problem. We give an affirmative answer: every nonnegative C^1 initial datum satisfying f_0(x,p)+|∇_x,pf_0(x,p)|≲⟨ x⟩^−a⟨ p⟩^−b, a>1, b>3, generates a unique global classical solution. No smallness or symmetry is assumed. The result covers finite and infinite mass and energy, including infinite kinetic energy density. The power thresholds are sharp for general pure-power bounds ensuring finite density and an absolutely convergent Coulomb field. The proof rests on two new mechanisms: local energy recovery for a population selected by energy growth, and a corrected moment--action closure based on nonnegative transverse interactions. The argument also yields global classical solutions of the nonrelativistic equation in the same initial class, allowing infinite mass with polynomial velocity tails of any order b>3.
ER -