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math.AP2026
A note on the non-existence of small non-trivial compact solutions for Euler-Poisson equation in 1D
Masaya Maeda, Tetsu Mizumachi
In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in D. The proof is based on the virial estimate w…
math.AP2026
Conditional asymptotic stability of solitary waves of the Euler-Poisson system on the line
Junsik Bae, Scipio Cuccagna, Masaya Maeda
We apply the idea of using a combination of virial inequalities and Kato smoothing, previously applied to NLS and generalized KdV pure power equations to Euler-Poisson: we assume t…