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Small solutions to nonlinear Schrödinger equations

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Small solutions to nonlinear Schrödinger equations ANNALES DE L’I. H. P., SECTION C CARLOS E. KENIG GUSTAVO PONCE LUIS VEGA Small solutions to nonlinear Schrödinger equations Annales de l’I. H. P., section C, tome 10, no 3 (1993), p. 255-288. <http://www.numdam.org/item?id=AIHPC_1993__10_3_255_0> © Gauthier-Villars, 1993, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section C » (http://www.elsevier.com/locate/anihpc), implique l’accord avec les condi- tions générales d’utilisation (http://www.numdam.org/legal.php). Toute uti- lisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Small solutions to nonlinear Schrödinger equations CARLOS E. KENIG* GUSTAVO PONCE* LUIS VEGA** Department of Mathematics University of Chicago Chicago, IL 60637, USA Department of Mathematics University of California Santa Barbara, CA 93106, USA Facultad de Ciencias Universidad Autonoma de Madrid Cantoblanco, Madrid 28049, Spain ABSTRACT. - It is shown that the initial value problem for the nonlinear Schrodinger equations where P (.) is a polynomial having no constant or linear terms, is locally well posed for a class of "small" data uo. The main ingredients in the proof are new estimates describing the smoothing effect of Kato type for the This method extends to systems and other dispersive models. Key words : Nonlinear Schrodinger equations, smoothing effects. Classification A .M.S. : 35 Q 20, 35 B 45, 44 B 99. * Supported in part by the NSF ** Supported in part by DGICYT. Annales de l’Institut Henri Poincaré - Analyse non linéaire - 0294-1449 Vol. 10/93/03/255/34/$5.40/ © Gauthier-Villars 256 C. E. KENIG, G. PONCE AND L. VEGA RESUME. - On montre que le probleme de Cauchy pour t’equation de S

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