Exponential stability of solutions to the Schrödinger-Poisson equation - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Exponential stability of solutions to the Schrödinger-Poisson equation

Résumé

We prove an exponential stability result for the small solutions of the Schrödinger-Poisson equation on the circle without exterior parameters in Gevrey class. More precisely we prove that for most of the initial data of Gevrey-norm smaller than $\varepsilon$ small enough, the solution of the Schrödinger-Poisson equation remains smaller than $2\varepsilon$ for times of order $exp(-\alpha |\log \varepsilon|^2 / \log |\log \varepsilon|)$. We stress out that this is the optimal time expected for PDEs as conjectured by Jean Bourgain in [Bou04].
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Dates et versions

hal-04256956 , version 1 (24-10-2023)
hal-04256956 , version 2 (06-11-2023)

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Joackim Bernier, Nicolas Camps, Benoît Grébert, Zhiqiang Wang. Exponential stability of solutions to the Schrödinger-Poisson equation. 2023. ⟨hal-04256956v1⟩
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