Local existence, global existence, and scattering for the nonlinear Schrodinger equation

被引：33

作者：

Cazenave, Thierry ^{[1
,2
]}

Naumkin, Ivan ^{[1
,2
]}

机构：

[1] Univ Paris 06, BC 187,4 Pl Jussieu, F-75252 Paris 05, France

[2] CNRS, Lab Jacques Louis Lions, BC 187,4 Pl Jussieu, F-75252 Paris 05, France

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2017年 / 19卷 / 02期

关键词：

Nonlinear Schrodinger equation; local existence; global existence; scattering; CAUCHY-PROBLEM;

D O I：

10.1142/S0219199716500383

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct for every alpha > 0 and gimel is an element of C a class of initial values u(0) for which there exists a local solution of the nonlinear Schrodinger equation iu(t) vertical bar Delta u vertical bar gimel vertical bar u vertical bar(alpha)u = 0 on R-N with the initial condition u(0, x) = u(0). Moreover, we construct for every alpha > 2/ N a class of (arbitrarily large) initial values for which there exists a global solution that scatters as t -> infinity.

引用

页数：20

共 17 条

[1]

Adams R., 2003, SOBOLEV SPACES

[2] NONEXISTENCE OF ASYMPTOTICALLY FREE SOLUTIONS FOR A NONLINEAR SCHRODINGER-EQUATION [J].