Bilinear Strichartz estimates for the ZK equation and applications
| Autor: | Molinet, Luc, Pilod, Didier |
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| Přispěvatelé: | Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Instituto de Matematica, Universidade Federal do Rio de Janeiro (UFRJ), Réseau Franco-Brésilien en Mathématiques, Université de Tours-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Annales de l'Institut Henri Poincaré (C) Non Linear Analysis Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2015, 32 (2), pp.347-371 |
| ISSN: | 0294-1449 |
| Popis: | International audience; We prove that the associated initial value problem is locally well-posed in $H^s(\mathbb R^2)$ for $s>\frac12$ and globally well-posed in $H^1(\mathbb R\times \mathbb T)$ and in $H^s(\R^3) $ for $ s>1$. Our main new ingredient is a bilinear Strichartz estimate in the context of Bourgain's spaces which allows to control the high-low frequency interactions appearing in the nonlinearity of \eqref{ZK0}. In the $\mathbb R^2$ case, we also need to use a recent result by Carbery, Kenig and Ziesler on sharp Strichartz estimates for homogeneous dispersive operators. Finally, to prove the global well-posedness result in $ \R^3 $, we need to use the atomic spaces introduced by Koch and Tataru. |
| Databáze: | OpenAIRE |
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