LONG RANGE SCATTERING AND MODIFIED WAVE OPERATORS FOR SOME HARTREE TYPE EQUATIONS I-Reference-Cited by-同舟云学术

LONG RANGE SCATTERING AND MODIFIED WAVE OPERATORS FOR SOME HARTREE TYPE EQUATIONS I

Published:2000-03 Issue:03 Volume:12 Page:361-429
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

GINIBRE J.¹,VELO G.²

Affiliation:

1. Laboratoire de Physique Théorique (Laboratoire associé au Centre National de la Recherche Scientifique - URA D0063), Université de Paris XI, Bâtiment 210, F-91405 Orsay Cedex, France

2. Dipartimento di Fisica, Universitá di Bologna and INFN, Sezione di Bologna, Italy

Abstract

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n≥3, including Hartree equations with potential V(x)= λ|x|-γ with γ<1. For 1/2<γ<1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X00000137

Reference19 articles.

1. Long-range scattering in the position representation

2. Ordinary differential equations, transport theory and Sobolev spaces

3. Long range scattering for non-linear Schrödinger and Hartree equations in space dimensionn≥2

4. On a class of non linear Schr�dinger equations with non local interaction

Cited by 35 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime;Evolution Equations and Control Theory;2023

2. Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation;Quarterly of Applied Mathematics;2022-03-15

3. Global Behavior of Solutions to the Focusing Generalized Hartree Equation;Michigan Mathematical Journal;2021-01-01

4. On the focusing generalized Hartree equation;Mathematics in Applied Sciences and Engineering;2020-12-16

5. Long range scattering for the Maxwell–Schrödinger system in the Lorenz gauge without any restriction on the size of data;Journal of Differential Equations;2020-08