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

被引:28
|
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
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.
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页数:20
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