Global well-posedness for a NLS-KdV system on T

Carlos Matheus

Keywords: Global well-posedness | Schrodinger-Korteweg-deVries system | I-method

We prove that the Cauchy problem of the Schrodinger - Korteweg - deVries (NLS-KdV) system on T is globally well-posed for initial data below the energy space $H^1\times H^1$. More precisely, we show that the non-resonant NLS-KdV is globally well-posed for initial data $(u_0,v_0)\in H^s\times H^s$ with $s>11/13$ and the resonant NLS-KdV is globally well-posed for initial data $(u_0,v_0)\in H^s\times H^s$ 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 $H^1\times H^1$.

Anexos:

• nls-kdv_global.pdf