GLOBAL EXISTENCE FOR THE CUBIC NONLINEAR SCHRODINGER EQUATION IN LOWER ORDER SOBOLEV SPACES

被引：0

作者：

Hayashi, Nakao ^{[1
]}

Naumkin, Pavel I. ^{[2
]}

机构：

[1] Osaka Univ, Dept Math, Grad Sch Sci, Toyonaka, Osaka 5600043, Japan

[2] Inst Matemat, Morelia 58089, Michoacan, Mexico

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2011年 / 24卷 / 9-10期

关键词：

SCATTERING;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for the cubic nonlinear Schrodinger equation {iu(t) + 1/2u(xx) = u(3), x is an element of R, t > 0, u(0, x) = u(0)(x), x is an element of R. (0.1) The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u(0) is an element of H(alpha) boolean AND H(0,alpha) with alpha >1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u(0) is an element of H(2) boolean AND H(0,2). Also we find the large-time asymptotics of solutions.

引用

页码：801 / 828

页数：28

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