A note on the nonlinear Schrodinger equation in weak Lp spaces

被引：36

作者：

Cazenave, T

Vega, L

Vilela, MC

机构：

[1] Univ Paris 06, UMR 7598, CNRS, F-75252 Paris 05, France

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

[3] Univ Alfonso X, Dept Matemat, Madrid 28691, Spain

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2001年 / 3卷 / 01期

关键词：

D O I：

10.1142/S0219199701000317

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the global Cauchy problem for the equation iu(t) + Deltau + lambda /u/(alpha)u = 0 in R-N Using generalized Strichartz' inequalities we show that, under some restrictions on alpha, if the initial value is sufficiently small in some weak L-p space then there exists a global solution. This result provides a common framework to the " classical " H-s solutions and to the self-similar solutions, thereby extending previous results by Planchon.

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页码：153 / 162

页数：10

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