no. 21-22
Partial Differential Equations
On the Davey–Stewartson system with singular initial data
[Le système de Davey–Stewartson à données singulières]

Présenté par : Gilles Lebeau

Villamizar-Roa, E.J.1 ; Pérez-López, J.E.1
1 Escuela de Matemáticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia
Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 959-964.

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 Lp-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-Lp spaces. In particular, we prove the existence of self-similar solutions. We also derive new results about scattering theory and asymptotic stability.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.033
Villamizar-Roa, E.J. 1 ; Pérez-López, J.E. 1

1 Escuela de Matemáticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia 
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Villamizar-Roa, E.J.; Pérez-López, J.E. On the Davey–Stewartson system with singular initial data. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 959-964. doi : 10.1016/j.crma.2012.10.033. http://www.numdam.org/articles/10.1016/j.crma.2012.10.033/

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