Solutions globales pour l'\'equation de Schr\"odinger cubique en dimension 3

The purpose of this article is to construct global solutions for some super-crtical Schrodinger equations using the theory of random data introduced by N.Burq and N.Tzvetkov. We begin our study by the cubic equation in three dimension. Thanks to the lens transform, it suffices to study a local theor...

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Bibliographic Details
Main Author Poiret, Aurélien
Format Journal Article
LanguageEnglish
Published 06.07.2012
Subjects
Mathematics - Analysis of PDEs
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Summary:The purpose of this article is to construct global solutions for some super-crtical Schrodinger equations using the theory of random data introduced by N.Burq and N.Tzvetkov. We begin our study by the cubic equation in three dimension. Thanks to the lens transform, it suffices to study a local theory for the Schr\"odinger equations with harmonic potential and we can establish Bourgain type bilinear estimates for the harmonic oscillator. Then, we explain how we can generalize this result in all dimensions.
DOI:10.48550/arxiv.1207.1578