Scattering theory for Hartree type equations
Annales de l'I.H.P. Physique théorique, Tome 46 (1987) no. 2, pp. 187-213. 
@article{AIHPA_1987__46_2_187_0,
     author = {Hayashi, Nakao and Tsutsumi, Yoshio},
     title = {Scattering theory for {Hartree} type equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {187--213},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {2},
     year = {1987},
     mrnumber = {887147},
     zbl = {0634.35059},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1987__46_2_187_0/}
}
TY  - JOUR
AU  - Hayashi, Nakao
AU  - Tsutsumi, Yoshio
TI  - Scattering theory for Hartree type equations
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1987
SP  - 187
EP  - 213
VL  - 46
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1987__46_2_187_0/
LA  - en
ID  - AIHPA_1987__46_2_187_0
ER  - 
%0 Journal Article
%A Hayashi, Nakao
%A Tsutsumi, Yoshio
%T Scattering theory for Hartree type equations
%J Annales de l'I.H.P. Physique théorique
%D 1987
%P 187-213
%V 46
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1987__46_2_187_0/
%G en
%F AIHPA_1987__46_2_187_0
Hayashi, Nakao; Tsutsumi, Yoshio. Scattering theory for Hartree type equations. Annales de l'I.H.P. Physique théorique, Tome 46 (1987) no. 2, pp. 187-213. http://archive.numdam.org/item/AIHPA_1987__46_2_187_0/

[1] J.E. Barab, Nonexistence of asymptotic free solutions for a nonlinear Schrödinger equation. J. Math. Phys., t. 25, 1984, p. 3270-3273. | MR | Zbl

[2] P. Brenner, On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations. Math. Z., t. 186, 1984, p. 383-391. | MR | Zbl

[3] P. Brenner, On scattering and everywhere defined scattering operators for non-linear Klein-Gordon equations. J. Differential Equations, t. 56, 1985, p. 310-344. | MR | Zbl

[4] J.M. Chadam and R.T. Glassey, Global existence of solutions to the Cauchy problem for time dependent Hartree equations. J. Math. Phys., t. 16, 1975, p. 1122-1130. | MR | Zbl

[5] A. Friedman, Partial Differential Equations. Holt-Rinehart and Winston, New York, 1969. | MR | Zbl

[6] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equation I, II. J. Funct. Anal, t. 32, 1979, p. 1-32, 33-71 ; III, Ann. Inst. Henri Poincaré, Physique Théorique, t. 28, 1978, p. 287-316. | Numdam | MR | Zbl

[7] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations with non local interactin. Math. Z., t. 170, 1980, p. 109-136. | MR | Zbl

[8] J. Ginibre and G. Velo, Sur une équation de Schrödinger non linéaire avec interaction non locale, in Nonlinear partial differential equations and their applications. Collège de France, Séminaire, vol. II, Pitman, Boston, 1981. | MR | Zbl

[9] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of non-linear Schrödinger equations, J. Math. pures et appl., t. 64, 1985, p. 363-401. | MR | Zbl

[10] R.T. Glassey, Asymptotic behavior of solutions to a certain nonlinear-Hartree equations, Comm. Math. Phys., t. 53, 1977, p. 9-18. | MR | Zbl

[11] N. Hayashi and M. Tsutsumi, L∞-decay of classical solutions for nonlinear Schrödinger equations, preprint.

[12] N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations, to appear in J. Funct. Anal. | MR | Zbl

[13] N. Hayashi and Y. Tsutsumi, Remarks on the scattering problem for nonlinear Schrödinger equations, preprint. | MR

[14] W. Hunziker, On the space-time behavior of Schrödinger wavefunctions. J. Math. Phys., t. 7, 1965, p. 300-304. | MR | Zbl

[15] A. Jensen, Commutator methods and a smoothing property of the Schrödinger evolution group. Math. Z., t. 191, 1986, p. 53-59. | MR | Zbl

[16] E.M. Stein, Singular Integral and Differentiability Properties of Functions, Princeton Univ. Press. Princeton Math. Series 30, 1970. | MR | Zbl

[17] W.A. Strauss, Nonlinear invariant wave equations, in Invariant Wave Equations (Erice, 1977), Lecture Notes in Physics, t. 78, Springer-Verlag, Berlin-Heidelberg- New York, 1978, p. 197-249. | MR

[18] W.A. Strauss, Nonlinear scattering theory at low energy. J. Funct. Anal., t. 41, 1981, p. 110-133. | MR | Zbl

[19] W.A. Strauss, Nonlinear Scattering theory at low energy: Sequel. J. Funct. Anal., t. 43, p. 281-293, | MR | Zbl

[20] R.S. Strichartz, Restrictions of Fourier Transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J., t. 44, 1977, p. 705-714. | MR | Zbl

[21] Y. Tsutsumi, Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations, Doctor Thesis, Univ. of Tokyo, 1985.

[22] Y. Tsutsumi, Scattering problem for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 43, 1985, p. 321-347. | Numdam | MR | Zbl

[23] Y. Tsutsumi and K. Yajima, The asymptotic behavior of nonlinear Schrödinger equations, Bull. (New Series). Amer. Math. Soc., t. 11, 1984, p. 186-188. | MR | Zbl

[24] K. Yajima, The surfboard Schrödinger equations. Comm. Math. Phys., t. 96, 1984, p. 349-360. | MR | Zbl

[25] J. Ginibre, Private communication.

[26] T. Kato, On nonlinear Schrödinger equations, preprint, University of California, Berkeley, 1986. | MR

[27] Y. Tsutsumi, L2-solutions for nonlinear Schrödinger equations and nonlinear groups, to appear in Funkcialaj Ekvacioj. | MR | Zbl