On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations

Nakao Hayashi; Keiichi Kato; Pavel I. Naumkin

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 27, Issue: 3-4, page 483-497
  • ISSN: 0391-173X

How to cite

top

Hayashi, Nakao, Kato, Keiichi, and Naumkin, Pavel I.. "On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 27.3-4 (1998): 483-497. <http://eudml.org/doc/84366>.

@article{Hayashi1998,
author = {Hayashi, Nakao, Kato, Keiichi, Naumkin, Pavel I.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {asymptotics for large time; Cauchy problem for the subcritical cubic nonlinear Schrödinger and Hartree type equations; sharp decay estimate},
language = {eng},
number = {3-4},
pages = {483-497},
publisher = {Scuola normale superiore},
title = {On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations},
url = {http://eudml.org/doc/84366},
volume = {27},
year = {1998},
}

TY - JOUR
AU - Hayashi, Nakao
AU - Kato, Keiichi
AU - Naumkin, Pavel I.
TI - On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 27
IS - 3-4
SP - 483
EP - 497
LA - eng
KW - asymptotics for large time; Cauchy problem for the subcritical cubic nonlinear Schrödinger and Hartree type equations; sharp decay estimate
UR - http://eudml.org/doc/84366
ER -

References

top
  1. [1] T. Cazenave, "An Introduction to Nonlinear Schrödinger Equations ", Textos de Métodos Mathemáticos, 22Univ. Federal do Rio de Janeiro, Instituto de Mathematica, 1989. 
  2. [2] T. Cazenave - F.B. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation in HS, Nonlinear Anal.14 (1990), 807-836. Zbl0706.35127MR1055532
  3. [3] P. D'Ancona - S. Spagnolo, Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math.108 (1992), 253-277. Zbl0785.35067MR1161092
  4. [4] J. Ginibre - T. Ozawa, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n &gt; 2, Comm. Math. Phys.151 (1993), 619-645. Zbl0776.35070MR1207269
  5. [5] J. Ginibre - G. Velo, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case; II. Scattering theory, general case, J. Funct. Anal.32 (1979), 1-71. Zbl0396.35029MR533218
  6. [6] N. Hayashi - E. Kaikina - P.I. Naumkin, On the scattering theory for the cubic nonlinear Schrödinger and Hartree type equations in one space dimension, Hokkaido Univ. Math. J.27 (1998), 651-667. Zbl0921.35163MR1662961
  7. [7] N. Hayashi - K. Kato, Global existence of small analytic solutions to Schrödinger equations with quadratic nonlinearity, Comm. Partial Differential Equations22 (1997), 773-798. Zbl0881.35106MR1452167
  8. [8] N. Hayashi - P.I. Naumkin, Asymptotics in large time of solutions to nonlinear Schrödinger and Hartree equations, Amer. J. Math.120 (1998), 369-389. Zbl0917.35128MR1613646
  9. [9] N. Hayashi - P.I. Naumkin, Scattering theory and large time asymptotics of solutions to the Hartree type equation with a long range potential, Preprint (1997). MR1815004
  10. [10] N. Hayashi - T. Ozawa, Scattering theory in the weighted L2(Rn) spaces for some Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor.48 (1988), 17-37. Zbl0659.35078MR947158
  11. [11] H. Hirata, The Cauchy problem for Hartree type Schrödinger equation in weighted Sobolev space, J. Faculty of Science, Univ. Tokyo, Sec IA 38 (1988), 567-588. Zbl0766.35053MR1146361
  12. [12] T. Kato - K. Masuda, Nonlinear evolution equations and analyticity I, Ann. Inst. H. Poincaré Anal. Non Linéaire3 (1986), 455-467. Zbl0622.35066MR870865
  13. [13] P.I. Naumkin, Asymptotics for large time of solutions to nonlinear Schrödinger equation, Izvestia61, n° 4 (1997), 81-118. Zbl0894.35103MR1480758
  14. [14] T. Ozawa, Long range scattering for nonlinear Schrödinger equations in one space dimension, Comm. Math. Phys.139 (1991), 479-493. Zbl0742.35043MR1121130

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.