A note on the non-existence of small non-trivial compact solutions for Euler-Poisson equation in 1D

Masaya Maeda; Tetsu Mizumachi

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arXiv · 2603.19662

A note on the non-existence of small non-trivial compact solutions for Euler-Poisson equation in 1D

Masaya Maeda·Tetsu Mizumachi

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Abstract

In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in $1$D. The proof is based on the virial estimate which provides local in space average decay of bounded small solutions.

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Masaya Maeda, Tetsu Mizumachi. 2026-03-20. A note on the non-existence of small non-trivial compact solutions for Euler-Poisson equation in 1D. https://arxiv.org/abs/2603.19662

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