Long range scattering and modified wave operators for some Hartree type equations I

Authors
Ginibre, J Velo, G
Citation
J. Ginibre et G. Velo, Long range scattering and modified wave operators for some Hartree type equations I, REV MATH PH, 12(3), 2000, pp. 361-429
Citations number
29
Categorie Soggetti
Physics
Journal title
REVIEWS IN MATHEMATICAL PHYSICS
ISSN journal
0129055X → ACNP
Volume
12
Issue
3
Year of publication
2000
Pages
361 - 429
Database
ISI
SICI code
0129-055X(200003)12:3<361:LRSAMW>2.0.ZU;2-V
Abstract
We study the theory of scattering for a class of Hartree type equations wit h long range interactions in space dimension n greater than or equal to 3, including Hartree equations with potential V(x) = lambda\x\(-gamma) with ga mma < 1. For 1/2 < gamma < 1 we prove the existence of modified wave operat ors with no size restriction on the data and we determine the asymptotic be haviour in time of solutions in the range of the wave operators.