A note on the non-$L^1$ asymptotic completeness of the Vlasov-Maxwell system

We prove that under a generic asymptotic condition on the charge, the small data solutions to the Vlasov-Maxwell system do not verify linear scattering. In other words, we show the non-$L^1$ asymptotic completeness of the system. The proof makes use of the Lorentz invariance of the equations.

Publication Details

Journal
ArXiv.org
Published
2025-09-04
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

A note on the non-$L^1$ asymptotic completeness of the Vlasov-Maxwell system

ArXiv.org
Geochemistry and Geologic Mapping
article

A note on the non-$L^1$ asymptotic completeness of the Vlasov-Maxwell system

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Abstract

We prove that under a generic asymptotic condition on the charge, the small data solutions to the Vlasov-Maxwell system do not verify linear scattering. In other words, we show the non-$L^1$ asymptotic completeness of the system. The proof makes use of the Lorentz invariance of the equations.

ArXiv.org
Openalex Percentile: Top 51%
Geochemistry and Geologic Mapping
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A note on the non-$L^1$ asymptotic completeness of the Vlasov-Maxwell system · ArXiv.org (2025) | TGRS Research Map | TGRS