Global well-posedness for Schrödinger equation with derivative in

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• 作者：Changxing Miao ; ^a ; ^{miao_changxing@iapcm.ac.cn"" rel=""nofollow} ; Yifei Wu^a ; ^{yerfmath@yahoo.cn"" rel=""nofollow} ; Guixiang Xu^a ; ^{xu_guixiang@iapcm.ac.cn"" rel=""nofollow}
• 关键词：Bourgain space ; DNLS equation ; Global well-posedness ; I-method ; Resonant decomposition
• 刊名：Journal of Differential Equations
• 出版年：2011
• 出版时间：15 October 2011
• 年：2011
• 卷：251
• 期：8
• 页码：2164-2195
• 全文大小：298 K

文摘

In this paper, we consider the Cauchy problem of the cubic nonlinear Schrödinger equation with derivative in . This equation was known to be the local well-posedness for (Takaoka, 1999 [27]), ill-posedness for (Biagioni and Linares, 2001 [1], etc.) and global well-posedness for (I-team, 2002 [10]). In this paper, we show that it is global well-posedness in the endpoint space , which remained open previously. The main approach is the third generation I-method combined with a new resonant decomposition technique. The resonant decomposition is applied to control the singularity coming from the resonant interaction.