GLOBAL WELL-POSEDNESS OF NLS-KDV SYSTEMS FOR PERIODIC FUNCTIONS

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 x H-1. More precisely, we show that the non-resonant NLS-KdV system is globally well-posed for initial data in H-s(T) x H-s(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.