Exponential stability of solutions to the Schrödinger-Poisson equation

2023/10/25 by Bernier, Joackim, Camps, Nicolas, Grébert, Benoît +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.16476

Abstract

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 ε small enough, the solution of the Schrödinger-Poisson equation remains smaller than 2ε for times of order exp(α|log ε|² / log |log ε|). We stress out that this is the optimal time expected for PDEs as conjectured by Jean Bourgain in [Bou04].

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• Nekhoroshev type stability for non-local semilinear Schrödinger equations

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