Smoothing effect for nonlinear Schrödinger equations in exterior domains
type: Item
instance of: scholarly article
title: Smoothing effect for nonlinear Schrödinger equations in exterior domains
zbMATH Open document ID: 0706.35128
DOI: 10.1016/0022-1236(90)90102-Q
author: Nakao Hayashi
published in: Journal of Functional Analysis
publication date: 1990-01-01T00:00:00Z
review text: We consider the following nonlinear Schrödinger equations in exterior domains: \[ (*)\quad i\partial_ tu+\Delta u=| u|^ 2u,\quad (t,x)\in {\mathbb{R}}\times D, \] \[ u(0,x)=\phi (x),\quad x\in D,\quad u(t,x)=0\quad (or\quad \partial u/\partial \nu =0),\quad (t,x)\in {\mathbb{R}}\times \partial D, \] where \(D=\{x\in {\mathbb{R}}^ n\); \(| x| >R\}\), \(\partial D=\{x\in {\mathbb{R}}^ n\); \(| x| =R\}\), \(R>0\), and \(\nu\) denotes the outward normal unit vector at \(x\in \partial D\). In this paper we prove that the radially symmetric solutions of (*) have a smoothing property.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 4159301
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: exterior domains
zbMATH Keywords: smoothing property
MaRDI profile type: Publication
cites work: Global existence of the solution of nonlinear Schrödinger equations in exterior domains
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description: scientific article; zbMATH DE number 4159301