PreprintCC BY 4.0arXiv
The relativistic Euler-Poisson equation as a mean-field limit
Abstract
We adapt the renormalized energy method developed in \cite{duerinckx2020mean} in order to prove the monokinetic mean field limit for relativistic Newtonian dynamics. The resulting monokinetic PDE is the relativistic Euler-Poisson equation. Since the position evolves relativistically in comparison to the momentum, the kinetic part of the modulated energy has to adjusted, leading to further obstructions that are not present in the non-relativistic settings. A weak-strong stability principle for the relativistic Euler-Poisson equation is investigated, followed by a renormalization procedure leading to the mean-field limit. Our main result constitute the first mean-field limit for relativistic Coulomb flows.
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BibTeX
@misc{porat2026relativistic,
title = {{The relativistic Euler-Poisson equation as a mean-field limit}},
author = {Immanuel Ben Porat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14880},
eprint = {2609.14880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14880},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The relativistic Euler-Poisson equation as a mean-field limit
AU - Immanuel Ben Porat
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14880
UR - https://arxiv.org/abs/2609.14880
AB - We adapt the renormalized energy method developed in \cite{duerinckx2020mean} in order to prove the monokinetic mean field limit for relativistic Newtonian dynamics. The resulting monokinetic PDE is the relativistic Euler-Poisson equation. Since the position evolves relativistically in comparison to the momentum, the kinetic part of the modulated energy has to adjusted, leading to further obstructions that are not present in the non-relativistic settings. A weak-strong stability principle for the relativistic Euler-Poisson equation is investigated, followed by a renormalization procedure leading to the mean-field limit. Our main result constitute the first mean-field limit for relativistic Coulomb flows.
ER -