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

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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

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  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

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