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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| Format | Journal Article |
| Language | English |
| Published |
06.07.2012
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| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Poiret, Aurélien |
| Author_xml | – sequence: 1 givenname: Aurélien surname: Poiret fullname: Poiret, Aurélien organization: LM-Orsay |
| BackLink | https://doi.org/10.48550/arXiv.1207.1578$$DView paper in arXiv |
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| Snippet | 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... |
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| SubjectTerms | Mathematics - Analysis of PDEs |
| Title | Solutions globales pour l'\'equation de Schr\"odinger cubique en dimension 3 |
| URI | https://arxiv.org/abs/1207.1578 |
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