Dispersive Estimates for Nonlinear Schrödinger Equations with External Potentials

We consider the long time dynamics of nonlinear Schr\"odinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Ou...

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Bibliographic Details
Published inarXiv.org
Main Author Dietze, Charlotte
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.04.2021
Subjects
Decay
Mathematical analysis
Nonlinear dynamics
Schrodinger equation
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Summary:We consider the long time dynamics of nonlinear Schr\"odinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel's formula.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.05502