1 9 N ov 2 00 5 GLOBAL WELL - POSEDNESS FOR A NLS - KDV SYSTEM ON T
نویسنده
چکیده
We prove that the Cauchy problem of the Schrödinger Korteweg deVries (NLS-KdV) system on T is globally well-posed for initial data (u0, v0) below the energy space H × H. More precisely, we show that the non-resonant NLS-KdV is globally wellposed for initial data (u0, v0) ∈ H (T)× H(T) with s > 11/13 and the resonant NLS-KdV is globally well-posed for initial data (u0, v0) ∈ H (T)×H(T) with s > 8/9. The idea of the proof of this theorem is to apply the I-method of Colliander, Keel, Staffilani, Takaoka and Tao in order to improve the results of Arbieto, Corcho and Matheus concerning the global well-posedness of the NLS-KdV on T in the energy space H × H.
منابع مشابه
Global Well-posedness of Nls-kdv Systems for Periodic Functions
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