Long range scattering and modified wave operators for Hartree equations
Journées équations aux dérivées partielles (1999), article no. 17, 9 p.

We study the theory of scattering for the Hartree equation with long range potentials. 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.

@article{JEDP_1999____A17_0,
     author = {Ginibre, Jean and Velo, Giorgio},
     title = {Long range scattering and modified wave operators for {Hartree} equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {17},
     pages = {1--9},
     publisher = {Universit\'e de Nantes},
     year = {1999},
     mrnumber = {2000h:35130},
     zbl = {01810590},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1999____A17_0/}
}
TY  - JOUR
AU  - Ginibre, Jean
AU  - Velo, Giorgio
TI  - Long range scattering and modified wave operators for Hartree equations
JO  - Journées équations aux dérivées partielles
PY  - 1999
SP  - 1
EP  - 9
PB  - Université de Nantes
UR  - http://www.numdam.org/item/JEDP_1999____A17_0/
LA  - en
ID  - JEDP_1999____A17_0
ER  - 
%0 Journal Article
%A Ginibre, Jean
%A Velo, Giorgio
%T Long range scattering and modified wave operators for Hartree equations
%J Journées équations aux dérivées partielles
%D 1999
%P 1-9
%I Université de Nantes
%U http://www.numdam.org/item/JEDP_1999____A17_0/
%G en
%F JEDP_1999____A17_0
Ginibre, Jean; Velo, Giorgio. Long range scattering and modified wave operators for Hartree equations. Journées équations aux dérivées partielles (1999), article  no. 17, 9 p. http://www.numdam.org/item/JEDP_1999____A17_0/

[1] T. Cazenave, An introduction to nonlinear Schrödinger equations, Text. Met. Mat. 26, Inst. Mat., Rio de Janeiro (1993).

[2] J. Derezinski, C. Gérard, Scattering Theory of Classical and Quantum N-Particle Systems, Springer, Berlin, 1997. | MR | Zbl

[3] J. Ginibre, T. Ozawa, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≥ 2, Commun. Math. Phys. 151 (1993), 619-645. | MR | Zbl

[4] J. Ginibre, G. Velo, On a class of nonlinear Schrödinger equations with non-local interaction, Math. Z. 170 (1980), 109-136. | EuDML | MR | Zbl

[5] J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations I, Rev. Math. Phys., to appear. | Zbl

[6] J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations II, Preprint, Orsay 1999. | Zbl

[7] N. Hayashi, P. I. Naumkin, Scattering theory and large time asymptotics of solutions to Hartree type equations with a long range potential, Preprint, 1997.

[8] N. Hayashi, P. I. Naumkin, Remarks on scattering theory and large time asymptotics of solutions to Hartree type equations with a long range potential, SUT J. of Math. 34 (1998), 13-24. | MR | Zbl

[9] N. Hayashi, Y. Tsutsumi, Scattering theory for Hartree type equations, Ann. IHP (Phys. Théor.) 46 (1987), 187-213. | EuDML | Numdam | MR | Zbl

[10] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. IV, Springer, Berlin, 1985. | Zbl

[11] H. Nawa, T. Ozawa, Nonlinear scattering with nonlocal interaction, Commun. Math. Phys. 146 (1992), 259-275. | MR | Zbl

[12] T. Ozawa, Long range scattering for nonlinear Schrödinger equations in one space dimension, Commun. Math. Phys. 139 (1991), 479-493. | MR | Zbl

[13] D.R. Yafaev, Wave operators for the Schrödinger equation, Theor. Mat. Phys. 45 (1980), 992-998. | MR | Zbl