Smoothing effect of small analytic solutions to nonlinear Schrödinger equations

Nakao Hayashi

Annales de l'I.H.P. Physique théorique (1992)

  • Volume: 57, Issue: 4, page 385-394
  • ISSN: 0246-0211

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Hayashi, Nakao. "Smoothing effect of small analytic solutions to nonlinear Schrödinger equations." Annales de l'I.H.P. Physique théorique 57.4 (1992): 385-394. <http://eudml.org/doc/76592>.

@article{Hayashi1992,
author = {Hayashi, Nakao},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {initial value problem; global solutions; smoothing property},
language = {eng},
number = {4},
pages = {385-394},
publisher = {Gauthier-Villars},
title = {Smoothing effect of small analytic solutions to nonlinear Schrödinger equations},
url = {http://eudml.org/doc/76592},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Hayashi, Nakao
TI - Smoothing effect of small analytic solutions to nonlinear Schrödinger equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1992
PB - Gauthier-Villars
VL - 57
IS - 4
SP - 385
EP - 394
LA - eng
KW - initial value problem; global solutions; smoothing property
UR - http://eudml.org/doc/76592
ER -

References

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  1. [1] P. Constantin and J.C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., Vol. 1, 1988, pp. 413-439. Zbl0667.35061MR928265
  2. [2] P. Constantin, Decay estimates for Schrödinger equations, Commun. Math. Phys., Vol. 127, 1990, pp. 101-108. Zbl0713.35090MR1036116
  3. [3] N. Hayashi, Global existence of small analytic solutions to nonlinear Schrödinger equations, Duke Math. J., Vol. 60, 1990, pp. 717-727. Zbl0721.35026MR1054532
  4. [4] N. Hayashi and S. Saitoh, Analyticity and global existence of small solutions to some nonlinear Schrödinger equations, Commun. Math. Phys., Vol. 129, 1990, pp. 27-42. Zbl0705.35132MR1046275
  5. [5] N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations, J. Funct. Anal., Vol. 71, 1987, pp. 218-245. Zbl0657.35033MR880978
  6. [6] H.P. McKean and J. Shatah, The nonlinear Schrödinger equation and the nonlinear heat equation: reduction to linear form, Commun. Pure Appl. Math., .Vol. 44, 1991, pp. 1067-1080. Zbl0773.35075MR1127050
  7. [7] E.M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971. Zbl0232.42007MR304972
  8. [8] C.E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations. Indiana Univ. Math. J., Vol. 40, 1991, pp. 33-69. Zbl0738.35022MR1101221
  9. [9] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J., Vol. 55, 1987, pp. 699-715. Zbl0631.42010MR904948
  10. [10] L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc., Vol. 102, 1988, pp. 874-878. Zbl0654.42014MR934859

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