Global wellposedness for 1D non-linear Schrodinger equation for data with an infinite L2 norm

被引：59

作者：

Vargas, A ^{[1
]}

Vega, L

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Basque Country, Dept Matemat, E-48080 Bilbao, Spain

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2001年 / 80卷 / 10期

关键词：

nonlinear Schrodinger; oscillatory integrals;

D O I：

10.1016/S0021-7824(01)01224-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove global wellposedness for the one-dimensional cubic non-linear Schrodinger equation in a space of distributions which is invariant under Galilean transformations and includes L-2. This space arises naturally in the study of the restriction properties of the Fourier transform to curved surfaces. The L-P bounds, p not equal 2, for the extension operator, dual to the restricition one, plays a fundamental role in our approach. (C) 2001 Editions scientifiques et medicales Elsevier SAS.

引用

页码：1029 / 1044

页数：16

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