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EnglishUsing suitable modified energies, we study higher-order Sobolev norms' growth in time for the nonlinear Schrödinger equation (NLS) on a generic 2- or 3-dimensional compact manifold. In two dimensions, we extend earlier results that dealt only with cubic nonlinearities, and get polynomial-in-time bounds for any higher-order nonlinearities. In three dimensions, we prove that solutions to the cubic NLS grow at most exponentially, while for the subcubic NLS we get polynomial bounds on the growth of the H2 norm.
| Autori interni: | |
| Autori: | Planchon, Fabrice; Tzvetkov, Nikolay; Visciglia, Nicola |
| Titolo: | On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds |
| Anno del prodotto: | 2017 |
| Abstract: | Using suitable modified energies, we study higher-order Sobolev norms' growth in time for the nonlinear Schrödinger equation (NLS) on a generic 2- or 3-dimensional compact manifold. In two dimensions, we extend earlier results that dealt only with cubic nonlinearities, and get polynomial-in-time bounds for any higher-order nonlinearities. In three dimensions, we prove that solutions to the cubic NLS grow at most exponentially, while for the subcubic NLS we get polynomial bounds on the growth of the H2 norm. |
| Digital Object Identifier (DOI): | 10.2140/apde.2017.10.1123 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| APDE-PTV.pdf | Versione finale editoriale | NON PUBBLICO - Accesso privato/ristretto | Utenti riconosciuti Richiedi una copia | |
| 1607.08903.pdf | Documento in Pre-print | Tutti i diritti riservati (All rights reserved) | Open AccessVisualizza/Apri |
http://hdl.handle.net/11568/876098
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