Scattering theory in the weighted L 2 ( n ) spaces for some Schrödinger equations

Nakao Hayashi; Tohru Ozawa

Annales de l'I.H.P. Physique théorique (1988)

  • Volume: 48, Issue: 1, page 17-37
  • ISSN: 0246-0211

How to cite

top

Hayashi, Nakao, and Ozawa, Tohru. "Scattering theory in the weighted $L^2 (\mathbb {R}^n)$ spaces for some Schrödinger equations." Annales de l'I.H.P. Physique théorique 48.1 (1988): 17-37. <http://eudml.org/doc/76388>.

@article{Hayashi1988,
author = {Hayashi, Nakao, Ozawa, Tohru},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {scattering problem; Schrödinger equation; asymptotically free; wave operators; scattering operator},
language = {eng},
number = {1},
pages = {17-37},
publisher = {Gauthier-Villars},
title = {Scattering theory in the weighted $L^2 (\mathbb \{R\}^n)$ spaces for some Schrödinger equations},
url = {http://eudml.org/doc/76388},
volume = {48},
year = {1988},
}

TY - JOUR
AU - Hayashi, Nakao
AU - Ozawa, Tohru
TI - Scattering theory in the weighted $L^2 (\mathbb {R}^n)$ spaces for some Schrödinger equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1988
PB - Gauthier-Villars
VL - 48
IS - 1
SP - 17
EP - 37
LA - eng
KW - scattering problem; Schrödinger equation; asymptotically free; wave operators; scattering operator
UR - http://eudml.org/doc/76388
ER -

References

top
  1. [1] J.E. Barab, Nonexistence of asymptotic free solutions for a nonlinear Schrödinger equation. J. Math. Phys., t. 25, 1984, p. 3270-3273. Zbl0554.35123MR761850
  2. [2] J. Bergh and J. Löfström, Interpolation Spaces. Berlin, Heidelberg, New York, Springer, 1976. Zbl0344.46071MR482275
  3. [3] A. Friedman, Partial Differential Equations. Holt-Rinehart and Winston, New York, 1969. Zbl0224.35002MR445088
  4. [4] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations 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. Zbl0396.35028MR533219
  5. [5] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear Schrödinger equations. J. Math. pures et appl., t. 64, 1985, p. 363-401. Zbl0535.35069MR839728
  6. [6] J. Ginibre and G. Velo, Private communication. 
  7. [7] N. Hayashi and Y. Tsutsumi, Scattering theory for Hartree type equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 46, 1987, p. 187-213. Zbl0634.35059MR887147
  8. [8] N. Hayashi and Y. Tsutsumi, Remarks on the scattering problem for nonlinear Schrödinger equations, to appear in the Proceedings of UAB conference on Differential Equations and Mathematical Physics, Springer-Verlag, New York, 1986. Zbl0633.35059MR921265
  9. [9] N. Hayashi and T. Ozawa, Time decay of solutions to the Cauchy problem for time-dependent Schrödinger-Hartree equations. Commun. Math. Phys., t. 110, 1987, p. 467-478. Zbl0648.35078MR891948
  10. [10] N. Hayashi and T. Ozawa, Smoothing effectfor some Schrödinger equations, preprint RIMS-583, 1987. MR1012208
  11. [11] N. Hayashi and T. Ozawa, Time decay for some Schrödinger equations, preprint RIMS-554, 1987. Zbl0648.35078MR987581
  12. [12] T. Kato, On nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 46, 1987, p. 113-129. Zbl0632.35038MR877998
  13. [13] E.M. Stein, Singular Integral and Differentiability Properties of Functions. Princeton Univ. Press, Princeton Math. Series30, 1970. Zbl0207.13501MR290095
  14. [14] W.A. Strauss, Decay and asymptotic for □u = F(u). J. Funct. Anal., t. 2, 1968, p. 409-457. Zbl0182.13602
  15. [15] W.A. Strauss, Nonlinear scattering theory at low energy: Sequel. J. Funct. Anal., t. 43, 1981, p. 281-293. Zbl0494.35068MR636702
  16. [16] Y. Tsutsumi, Scattering problem for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 43, 1985, p. 321-347. Zbl0612.35104MR824843
  17. [17] Y. Tsutsumi and K. Yajima, The asymptotic behavior of nonlinear Schrödinger equations. Bull. (New Series), Amer. Math. Soc., t. 11, 1984, p. 186-188. Zbl0555.35028MR741737
  18. [18] K. Yajima, Existence of solutions for Schrödinger evolution equations. Commun. Math. Phys., t. 110, 1987, p. 415-426. Zbl0638.35036MR891945
  19. [19] J. Ginibre, A remark on some papers by N. Hayashi and T. Ozawa, preprint Or say, 1987. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.