Local existence, global existence, and scattering for the nonlinear Schrodinger equation
被引:28
|
作者:
Cazenave, Thierry
论文数: 0引用数: 0
h-index: 0
机构:
Univ Paris 06, BC 187,4 Pl Jussieu, F-75252 Paris 05, France
CNRS, Lab Jacques Louis Lions, BC 187,4 Pl Jussieu, F-75252 Paris 05, FranceUniv Paris 06, BC 187,4 Pl Jussieu, F-75252 Paris 05, France
Cazenave, Thierry
[1
,2
]
Naumkin, Ivan
论文数: 0引用数: 0
h-index: 0
机构:
Univ Paris 06, BC 187,4 Pl Jussieu, F-75252 Paris 05, France
CNRS, Lab Jacques Louis Lions, BC 187,4 Pl Jussieu, F-75252 Paris 05, FranceUniv Paris 06, BC 187,4 Pl Jussieu, F-75252 Paris 05, France
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
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.