Global well-posedness for a NLS-KdV system on $\mathbb{T}$
| dc.creator | Matheus, Carlos | |
| dc.date | 2005-11-19 | |
| dc.date.accessioned | 2026-07-07T06:51:29Z | |
| dc.date.available | 2026-07-07T06:51:29Z | |
| dc.description | We prove that the Cauchy problem of the Schrödinger - Korteweg - deVries (NLS-KdV) system on $\mathbb{T}$ is globally well-posed for initial data $(u_0,v_0)$ 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 $(u_0,v_0)\in H^s(\mathbb{T})\times H^s(\mathbb{T})$ with $s>11/13$ and the resonant NLS-KdV is globally well-posed for initial data $(u_0,v_0)\in H^s(\mathbb{T})\times H^s(\mathbb{T})$ 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 $\mathbb{T}$ in the energy space $H^1\times H^1$. | |
| dc.identifier | https://arxiv.org/abs/math/0511492 | |
| dc.identifier | http://arxiv.org/abs/math/0511492 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105002 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q99 | |
| dc.title | Global well-posedness for a NLS-KdV system on $\mathbb{T}$ | |
| dc.type | text |