Electron. J. Diff. Eqns., Vol. 2007(2007), No. 07, pp. 1-20.

Global well-posedness of NLS-KdV systems for periodic functions

Carlos Matheus

Abstract:
We prove that the Cauchy problem of the Schrodinger-Korteweg-deVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space $H^1\times H^1$. More precisely, we show that the non-resonant NLS-KdV system is globally well-posed for initial data in $H^s(\mathbb{T})\times H^s(\mathbb{T})$ with s>11/13 and the resonant NLS-KdV system is globally well-posed with s>8/9. The strategy is to apply the I-method used by Colliander, Keel, Staffilani, Takaoka and Tao. By doing this, we improve the results by Arbieto, Corcho and Matheus concerning the global well-posedness of NLS-KdV systems.

Submitted November 13, 2006. Published January 2, 2007.
Math Subject Classifications: 35Q55.
Key Words: Global well-posedness; Schrodinger-Korteweg-de Vries system; I-method.

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Carlos Matheus
Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Estrada Dona Castorina 110
Rio de Janeiro, 22460-320, Brazil
email: matheus@impa.br

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