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| HAL : hal-00697812, version 1 |
| arXiv : 1205.3615 |
| Fiche détaillée |  Récupérer au format |
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| On the Cauchy problem for Hartree equation in the Wiener algebra |
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| Rémi Carles 1Lounes Mouzaoui 1 |
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| (16/05/2012) |
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| We consider the mass-subcritical Hartree equation with a homogeneous kernel, in the space of square integrable functions whose Fourier transform is integrable. We prove a global well-posedness result in this space. On the other hand, we show that the Cauchy problem is not even locally well-posed if we simply work in the space of functions whose Fourier transform is integrable. Similar results are proven when the kernel is not homogeneous, and is such that its Fourier transform belongs to some Lebesgue space. |
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| 1 : | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et techniques |
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| Analyse, Calcul Scientifique Industriel et Optimisation de Montpellier (ACSIOM) |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| hal-00697812, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00697812 | |
| oai:hal.archives-ouvertes.fr:hal-00697812 | |
| Contributeur : Rémi Carles | |
| Soumis le : Mercredi 16 Mai 2012, 11:43:13 | |
| Dernière modification le : Mercredi 16 Mai 2012, 11:46:22 | |
