Global well-posedness for a NLS-KdV system on $\mathbb{T}$

dc.creatorMatheus, Carlos
dc.date2005-11-19
dc.date.accessioned2026-07-07T06:51:29Z
dc.date.available2026-07-07T06:51:29Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/math/0511492
dc.identifierhttp://arxiv.org/abs/math/0511492
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105002
dc.subjectAnalysis of PDEs
dc.subject35Q99
dc.titleGlobal well-posedness for a NLS-KdV system on $\mathbb{T}$
dc.typetext

Files

Collections