On the existence of the wave operators for a class of nonlinear Schrödinger equations
Ginibre, J. ; Ozawa, T. ; Velo, G.
Annales de l'I.H.P. Physique théorique, Tome 61 (1994), p. 211-239 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1994__60_2_211_0,
     author = {Ginibre, Jean and Ozawa, Tohru and Velo, Giorgio},
     title = {On the existence of the wave operators for a class of nonlinear Schr\"odinger equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {61},
     year = {1994},
     pages = {211-239},
     mrnumber = {1270296},
     zbl = {0808.35136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1994__60_2_211_0}
}

Ginibre, J.; Ozawa, T.; Velo, G. On the existence of the wave operators for a class of nonlinear Schrödinger equations. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) pp. 211-239. http://gdmltest.u-ga.fr/item/AIHPA_1994__60_2_211_0/

[1] J.E. Barab, Nonexistence of Asymptotically Free Solutions for Nonlinear Schrödinger Equation, J. Math. Phys., Vol. 25, 1984, pp. 3270-3273. | MR 761850 | Zbl 0554.35123

[2] J. Bergh and J. Löfström, Interpolation Spaces, Berlin, Springer, 1976. | MR 482275 | Zbl 0344.46071

[3] T. Cazenave, An Introduction to Nonlinear Schrödinger Equations, Textos de Métodos Matematicos, Vol. 22, Instituto de Matematica, Rio de Janeiro, 1989.

[4] T. Cazenave and F. Weissler, The Cauchy Problem for the Critical Nonlinear Schrödinger Equation in Hs, Nonlin. Anal. TMA, Vol. 14, 1990, pp. 807-836. | MR 1055532 | Zbl 0706.35127

[5] T. Cazenave and F. Weissler, Rapidly Decaying Solutions of the Nonlinear Schrödinger Equation, Commun. Math. Phys., Vol. 147, 1992, p. 75-100. | MR 1171761 | Zbl 0763.35085

[6] J. Ginibre and T. Ozawa, Long Range Scattering for Nonlinear Schrödinger and Hartree Equations in Space Dimension n≧2, Commun. Math. Phys., Vol. 151, 1993, pp. 619-645. | MR 1207269 | Zbl 0776.35070

[7] J. Ginibre and G. Velo, On a Class of Nonlinear Schrödinger Equations I. The Cauchy Problem General Case, J. Funct. Anal., Vol. 32, 1979, p. 1-32. | MR 533218 | Zbl 0396.35028

[8] J. Ginibre and G. Velo, On a Class of Nonlinear Schrödinger Equations II. Scattering Theory, General Case, J. Funct. Anal., Vol. 32, 1979, pp. 33-71. | MR 533219 | Zbl 0396.35029

[9] J. Ginibre and G. Velo, Scattering Theory in the Energy Space for a Class of Nonlinear Schrödinger Equations, J. Math. Pures Appl., Vol. 64, 1985, p. 363-401. | MR 839728 | Zbl 0535.35069

[10] J. Ginibre and G. Velo, The Global Cauchy Problem for the Nonlinear Klein-Gordon Equation, Math. Z., Vol. 189, 1985, pp. 487-505. | MR 786279 | Zbl 0549.35108

[11] J. Ginibre and G. Velo, Time Decay of Finite Energy Solutions of the Nonlinear Klein Gordon and Schrödinger Equations, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 43, 1985, pp. 399-442. | Numdam | MR 824083 | Zbl 0595.35089

[12] J. Ginibre and G. Velo, Scattering Theory in the Energy Space for a Class of Nonlinear Wave Equations, Commun. Math. Phys., Vol. 123, 1989, pp. 535-573. | MR 1006294 | Zbl 0698.35112

[13] J. Ginibre and G. Velo, Smoothing Properties and Retarded Estimates for Some Dispersive Evolution Equations, Commun. Math. Phys., Vol. 144, 1992, pp. 163-188. | MR 1151250 | Zbl 0762.35008

[14] N. Hayashi and M. Tsutsumi, L∞ (Rn)-Decay of Classical Solutions for Non Linear Schrödinger Equations, Proceedings of the Royal Society of Edinburgh, Vol. 104, 1986, pp. 309-327. | MR 877907 | Zbl 0651.35014

[15] N. Hayashi and Y. Tsutsumi, Remarks on the Scattering Problem for Nonlinear Schrödinger Equations, Lecture Notes in Math., Vol. 1285, 1987, Springer, pp. 162- 168. | MR 921265 | Zbl 0633.35059

[16] T. Kato, On Nonlinear Schrödinger Equations, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 46, 1987, pp. 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[17] T. Kato, Nonlinear Schrödinger Equations, in: Schrödinger Operators, Lect. Notes Phys., Vol. 345, Springer, 1989. | MR 1037322 | Zbl 0698.35131

[18] J.E. Lin and W.A. Strauss, Decay and Scattering of Solutions of a Nonlinear Schrödinger Equation, J. Funct. Anal., Vol. 30, 1978, pp. 245-263. | MR 515228 | Zbl 0395.35070

[19] H.P. Mckean and J. Shatah, The Nonlinear Schrödinger Equation and the Nonlinear Heat Equation; Reduction to Linear Form, Comm. Pure Appl. Math., Vol. 44, 1991, pp. 1067-1080. | MR 1127050 | Zbl 0773.35075

[20] H. Nawa and T. Ozawa, Nonlinear Scattering with Non Local Interaction, Commun. Math. Phys., Vol. 146, 1992, pp. 259-275. | MR 1165183 | Zbl 0748.35046

[21] T. Ozawa, Long Range Scattering for Nonlinear Schrödinger Equations in One Space Dimension, Commun. Math. Phys., Vol. 139, 1991, pp. 479-493. | MR 1121130 | Zbl 0742.35043

[22] W.A. Strauss, Nonlinear Scattering Theory, in Scattering Theory in Mathematical Physics, J. LAVITA, J. P. MARCHAND, eds, Reidel, 1974. | Zbl 0297.35062

[23] W.A. Strauss, Nonlinear Scattering Theory at Low Energy, J. Funct. Anal., Vol. 41, 1981, pp. 110-133. | MR 614228 | Zbl 0466.47006

[24] Y. Tsutsumi, Scattering Problem for Nonlinear Schrödinger Equations, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 43, 1985, pp. 321-347. | Numdam | MR 824843 | Zbl 0612.35104

[25] Y. Tsutsumi, Global Existence and Asymptotic Behavior of Solutions for Nonlinear Schrödinger Equations, Doctoral Thesis, University of Tokyo, 1985.

[26] Y. Tsutsumi, L2 Solutions for Nonlinear Schrödinger Equations and Nonlinear Groups, Funkcialaj Ekvacioj, Vol. 30, 1987, pp. 115-125. | MR 915266 | Zbl 0638.35021

[27] Y. Tsutsumi and K. Yajima, The asymptotic Behavior of Nonlinear Schrödinger Equations, Bull. Am. Math. Soc., Vol. 11, 1984, pp. 186-188. | MR 741737 | Zbl 0555.35028

[28] K. Yajima, Existence of Solutions for Schrödinger Evolution Equations, Commun. Math. Phys., Vol. 110, 1987, pp. 415-426. | MR 891945 | Zbl 0638.35036

[29] H. Triebel, Theory of Function Spaces, Birkhauser, 1983. | Zbl 0546.46027