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| HAL : hal-00700699, version 1 |
| arXiv : 1205.4943 |
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| Modified wave operators without loss of regularity for some long range Hartree equations. I |
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| J. Ginibre 1G. Velo 2 |
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| (22/05/2012) |
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| We reconsider the theory of scattering for some long range Hartree equations with potential |x|^-gamma with 1/2 < gamma < 1. More precisely we study the local Cauchy problem with infinite initial time, which is the main step in the construction of the modified wave operators. We solve that problem in the whole subcritical range without loss of regularity between the asymptotic state and the solution, thereby recovering a result of Nakanishi. Our method starts from a different parametrization of the solutions, already used in our previous papers. This reduces the proofs to energy estimates and avoids delicate phase estimates. |
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| 1 : | Laboratoire de Physique Théorique d'Orsay (LPT) |
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CNRS : UMR8627 – Université Paris XI - Paris Sud |
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| 2 : | Dipartimento di Fisica |
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INFN – Università degli studi di Bologna |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Physique/Physique mathématique Mathématiques/Physique mathématique |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1205.4943 |
| hal-00700699, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00700699 | |
| oai:hal.archives-ouvertes.fr:hal-00700699 | |
| Contributeur : Patricia Dubois-Violette | |
| Soumis le : Mercredi 23 Mai 2012, 16:32:40 | |
| Dernière modification le : Mercredi 23 Mai 2012, 16:32:40 | |
