Analyticity and global existence of small solutions to some nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: Analyticity and global existence of small solutions to some nonlinear Schrödinger equations
zbMATH Open document ID: 0705.35132
DOI: 10.1007/BF02096777
author: Nakao Hayashi
author: S. Saitoh
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: L'auteur étudie l'existence de solutions du problème suivant: \[ i\partial_ tu+\Delta u=| u|^ 2u,\quad (t,x)\in {\mathbb{R}}\times {\mathbb{R}}^ n;\quad u(0,x)=\phi (x). \] (Problème initial pour une équation de Schrödinger nonlinéaire.) Il étudie aussi la regularité d'une telle solution. Il considère 2 cas: 1) Si \(\phi \in H^{2n+1}({\mathbb{R}}^ n)\) et si \(\phi\) decroît exponentiellement à l'infini, alors le problème considéré, admet une solution globale, analytique en x, pour \(t\neq 0\) (en supposant qu'une norme convenable de \(\phi\) est assez petite. 2) Si \(\phi\) est analytique, de norme (convenable) petite, alors il existe une solution globale analytique en x.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 4157132
zbMATH Keywords: Cauchy problem
zbMATH Keywords: small data
zbMATH Keywords: global analytic solution
MaRDI profile type: Publication
cites work: Q4119542
cites work: On the initial value problem for a nonlinear Schrödinger equation
cites work: On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
cites work: Classical solutions of nonlinear Schrödinger equations
cites work: On solutions on the initial value problem for the nonlinear Schrödinger equations
cites work: Nonlinear evolution equations and analyticity. I
cites work: Long-time behavior of solutions to nonlinear evolution equations
cites work: Global, small amplitude solutions to nonlinear evolution equations
cites work: Global existence of small solutions to nonlinear evolution equations
cites work: Wave operators and analytic solutions for systems of nonlinear Klein- Gordon equations and of nonlinear Schrödinger equations
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description: scientific article; zbMATH DE number 4157132