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 . More precisely, we show that the non-resonant NLS-KdV system is globally well-posed for initial data in 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
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