Long range scattering and modified wave operators for Hartree equations

Jean Ginibre; Giorgio Velo

Journées équations aux dérivées partielles (1999)

  • page 1-9
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Ginibre, Jean, and Velo, Giorgio. "Long range scattering and modified wave operators for Hartree equations." Journées équations aux dérivées partielles (1999): 1-9. <http://eudml.org/doc/93374>.

@article{Ginibre1999,
abstract = {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.},
author = {Ginibre, Jean, Velo, Giorgio},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-9},
publisher = {Université de Nantes},
title = {Long range scattering and modified wave operators for Hartree equations},
url = {http://eudml.org/doc/93374},
year = {1999},
}

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
PB - Université de Nantes
SP - 1
EP - 9
AB - 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.
LA - eng
UR - http://eudml.org/doc/93374
ER -

References

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  1. [1] T. Cazenave, An introduction to nonlinear Schrödinger equations, Text. Met. Mat. 26, Inst. Mat., Rio de Janeiro (1993). 
  2. [2] J. Derezinski, C. Gérard, Scattering Theory of Classical and Quantum N-Particle Systems, Springer, Berlin, 1997. Zbl0899.47007MR99d:81172
  3. [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. Zbl0776.35070MR93m:35168
  4. [4] J. Ginibre, G. Velo, On a class of nonlinear Schrödinger equations with non-local interaction, Math. Z. 170 (1980), 109-136. Zbl0407.35063MR82c:35018
  5. [5] J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations I, Rev. Math. Phys., to appear. Zbl1044.35041
  6. [6] J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations II, Preprint, Orsay 1999. Zbl1067.35501
  7. [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. Zbl0937.35167
  8. [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. Zbl0937.35167MR99i:35147
  9. [9] N. Hayashi, Y. Tsutsumi, Scattering theory for Hartree type equations, Ann. IHP (Phys. Théor.) 46 (1987), 187-213. Zbl0634.35059MR89a:81158
  10. [10] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. IV, Springer, Berlin, 1985. Zbl0601.35001
  11. [11] H. Nawa, T. Ozawa, Nonlinear scattering with nonlocal interaction, Commun. Math. Phys. 146 (1992), 259-275. Zbl0748.35046MR93f:35170
  12. [12] T. Ozawa, Long range scattering for nonlinear Schrödinger equations in one space dimension, Commun. Math. Phys. 139 (1991), 479-493. Zbl0742.35043MR92j:35172
  13. [13] D.R. Yafaev, Wave operators for the Schrödinger equation, Theor. Mat. Phys. 45 (1980), 992-998. Zbl0467.35076MR82j:35119

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