PreprintCC BY 4.0arXiv
From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit
Abstract
We derive the pressureless Euler-Maxwell system as a semiclassical limit from the Maxwell-Schrödinger equation. The method relies on studying a quantum modulated energy accounting for the self-consistent magnetic effects. Crucially, a correction is incorporated in the quantum modulated energy as to enable to close the Grönwall estimate provided a smallness assumption on the initial data is imposed. This is the first result on the semiclassical limit of the Maxwell-Schrödinger equation avoiding any regularization or conditional uniform in ℏ bounds on the wave
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BibTeX
@misc{porat2026from,
title = {{From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit}},
author = {Immanuel Ben Porat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11199},
eprint = {2610.11199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11199},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit
AU - Immanuel Ben Porat
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11199
UR - https://arxiv.org/abs/2610.11199
AB - We derive the pressureless Euler-Maxwell system as a semiclassical limit from the Maxwell-Schrödinger equation. The method relies on studying a quantum modulated energy accounting for the self-consistent magnetic effects. Crucially, a correction is incorporated in the quantum modulated energy as to enable to close the Grönwall estimate provided a smallness assumption on the initial data is imposed. This is the first result on the semiclassical limit of the Maxwell-Schrödinger equation avoiding any regularization or conditional uniform in ℏ bounds on the wave
ER -