On the Davey–Stewartson system with singular initial data

E.J. Villamizar-Roa; J.E. Pérez-López

doi:10.1016/j.crma.2012.10.033

Partial Differential Equations

On the Davey–Stewartson system with singular initial data
[Le système de Davey–Stewartson à données singulières]

Présenté par : Gilles Lebeau

E.J. Villamizar-Roa ¹ ; J.E. Pérez-López ¹

¹ Escuela de Matemáticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia

Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 959-964.

Résumé
Abstract

On étude lʼexistence des solutions locales et globales du système de Davey–Stewartson avec des donnés initiales dans les spaces de Lorentz, y comprenant les spaces $L^{p}$ -faibles. En particulier, on prouve lʼexistence des solutions auto-similaires. On dérive aussi des nouveux résultats sur la théorie de scattering et sur la stabilité asymptotique.

We study the existence of local and global solutions for the Davey–Stewartson system with initial data in Lorentz spaces, including weak- $L^{p}$ spaces. In particular, we prove the existence of self-similar solutions. We also derive new results about scattering theory and asymptotic stability.

Reçu le : 2012-08-15
Accepté le : 2012-10-31
Publié le : 2012-11-01

DOI : 10.1016/j.crma.2012.10.033

Affiliations des auteurs :

E.J. Villamizar-Roa ¹ ; J.E. Pérez-López ¹

¹ Escuela de Matemáticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia

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     title = {On the {Davey{\textendash}Stewartson} system with singular initial data},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {959--964},
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E.J. Villamizar-Roa; J.E. Pérez-López. On the Davey–Stewartson system with singular initial data. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 959-964. doi : 10.1016/j.crma.2012.10.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.033/

Bibliographie
Cité par

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