WELL-POSEDNESS AND SMOOTHING EFFECT FOR GENERALIZED NONLINEAR SCHRODINGER EQUATIONS

被引：0

作者：

Bienaime, Pierre-Yves ^{[1
]}

Boulkhemair, Abdesslam ^{[1
]}

机构：

[1] Univ Nantes, Lab Math Jean Leray, CNRS, UMR6629, Nantes, France

来源：

ANALYSIS & PDE | 2018年 / 11卷 / 05期

关键词：

Cauchy problem; well-posedness; smoothing effect; nonlinear equation; Schrodinger; paradifferential; pseudodifferential; operator; paralinearization; CAUCHY-PROBLEM; LOCAL EXISTENCE;

D O I：

10.2140/apde.2018.11.1241

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We improve the result obtained by one of the authors, Bienaime (2014), and establish the well-posedness of the Cauchy problem for some nonlinear equations of Schrodinger type in the usual Sobolev space H-s (R-n) for s > n/2 + 2 instead of s > n/2+ 3. We also improve the smoothing effect of the solution and obtain the optimal exponent.

引用

页码：1241 / 1284

页数：44

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