Comptes Rendus
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

E.J. Villamizar-Roa1 ; J.E. Pérez-López1
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.

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

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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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/

[1] V. Barros The Davey Stewartson system in weak Lp spaces, Differential Integral Equations, Volume 25 (2012), pp. 883-898

[2] J. Bergh; J. Löfström Interpolation Spaces, Springer-Verlag, Berlin–New York, 1976

[3] P. Braz e Silva; L.C.F. Ferreira; E.J. Villamizar-Roa On the existence of infinite energy solutions for nonlinear Schrödinger equations, Proc. Amer. Math. Soc., Volume 137 (2009), pp. 1977-1987

[4] A. Davey; K. Stewartson On three-dimensional packets of surface waves, Proc. R. Soc. Lond. Ser. A, Volume 338 (1974), pp. 101-110

[5] L.C.F. Ferreira; E.J. Villamizar-Roa Self-similarity and asymptotic stability for coupled nonlinear Schrödinger equations in high dimensions, Physica D, Volume 241 (2012), pp. 534-542

[6] J.M. Ghidaglia; J.C. Saut On the initial value problem for the Davey–Stewartson systems, Nonlinearity, Volume 3 (1990), pp. 475-506

[7] X. Li; J. Zhang; S. Lai; Y. Wu The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system, J. Differential Equations, Volume 250 (2011), pp. 2197-2226

[8] X. Zhao Self-similar solutions to a generalized Davey–Stewartson system, Math. Comput. Modelling, Volume 50 (2009), pp. 1394-1399

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