The Cauchy problem for the Schrödinger–KdV system

详细信息    查看全文

• 作者：Hua Wang^a ; ^b ; ^{wanghua_math@126.com} ; Shangbin Cui^c ; ^{cuisb3@yahoo.com.cn}
• 关键词：Local well-posedness ; Schr&#xf6 ; dinger– ; Korteweg– ; de Vries system ; Bilinear estimates
• 刊名：Journal of Differential Equations
• 出版年：2011
• 出版时间：1 May 2011
• 年：2011
• 卷：250
• 期：9
• 页码：3559-3583
• 全文大小：274 K

文摘

In this paper we prove that in the general case (i.e. β not necessarily vanishing) the Cauchy problem for the Schrödinger–Korteweg–de Vries system is locally well-posed in , and if β=0 then it is locally well-posed in with . These results improve the corresponding results of Corcho and Linares (2007) [5]. Idea of the proof is to establish some bilinear and trilinear estimates in the space G^s×F^s, where G^s and F^s are dyadic Bourgain-type spaces related to the Schrödinger operator and the Airy operator , respectively, but with a modification on F^s in low frequency part of functions with a weaker structure related to the maximal function estimate of the Airy operator.