Smoothing effect of small analytic solutions to nonlinear Schrödinger equations
Hayashi, Nakao
Annales de l'I.H.P. Physique théorique, Tome 56 (1992), p. 385-394 / Harvested from Numdam
Publié le : 1992-01-01
@article{AIHPA_1992__57_4_385_0,
     author = {Hayashi, Nakao},
     title = {Smoothing effect of small analytic solutions to nonlinear Schr\"odinger equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {56},
     year = {1992},
     pages = {385-394},
     mrnumber = {1198983},
     zbl = {0766.35052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1992__57_4_385_0}
}
Hayashi, Nakao. Smoothing effect of small analytic solutions to nonlinear Schrödinger equations. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) pp. 385-394. http://gdmltest.u-ga.fr/item/AIHPA_1992__57_4_385_0/

[1] P. Constantin and J.C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., Vol. 1, 1988, pp. 413-439. | MR 928265 | Zbl 0667.35061

[2] P. Constantin, Decay estimates for Schrödinger equations, Commun. Math. Phys., Vol. 127, 1990, pp. 101-108. | MR 1036116 | Zbl 0713.35090

[3] N. Hayashi, Global existence of small analytic solutions to nonlinear Schrödinger equations, Duke Math. J., Vol. 60, 1990, pp. 717-727. | MR 1054532 | Zbl 0721.35026

[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. | MR 1046275 | Zbl 0705.35132

[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. | MR 880978 | Zbl 0657.35033

[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. | MR 1127050 | Zbl 0773.35075

[7] E.M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971. | MR 304972 | Zbl 0232.42007

[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. | MR 1101221 | Zbl 0738.35022

[9] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J., Vol. 55, 1987, pp. 699-715. | MR 904948 | Zbl 0631.42010

[10] L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc., Vol. 102, 1988, pp. 874-878. | MR 934859 | Zbl 0654.42014