Global well-posedness of NLS-KdV systems for periodic functions
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We prove that the Cauchy problem of the Schrödinger-Korteweg-deVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1 x H1. More precisely, we show that the non-resonant NLS-KdV system is globally well-posed for initial data in Hs(T) x Hs(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.
CitationMatheus, C. (2021). Global well-posedness of NLS-KdV systems for periodic functions. Electronic Journal of Differential Equations, 2007(07), pp. 1-20.
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