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arXiv · 2310.16476

Exponential stability of solutions to the Schr{\"o}dinger-Poisson equation

Joackim Bernier·Nicolas Camps·Benoît Grébert·Zhiqiang Wang
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Abstract

We prove an exponential stability result for the small solutions of the Schr{\"o}dinger-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 Schr{\"o}dinger-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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Joackim Bernier, Nicolas Camps, Benoît Grébert, Zhiqiang Wang. 2023-10-25. Exponential stability of solutions to the Schr{\"o}dinger-Poisson equation. https://arxiv.org/abs/2310.16476

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