Modified wave operators for the Hartree equation with data, image and convergence in the same space
type: Item
instance of: scholarly article
title: Modified wave operators for the Hartree equation with data, image and convergence in the same space
zbMATH Open document ID: 1013.35056
author: Kenji Nakanishi
published in: Communications on Pure and Applied Analysis
publication date: 2003-06-24T00:00:00Z
review text: As is well known the wave operators do not exist for the Hartree equation with long-range potential \(|x|^{-1}\), i.e., the nontrivial solutions do not approach to any free solutions as time goes to plus and minus infinity. In this paper the author constructs appropriately modified wave operators that are defined on the space \( (1+|x|)^{-s} L^2, s > 1/2\). The results imply, in particular, asymptotic completeness for small data.
reviewed by: Ricardo Weder
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 1833242
zbMATH Keywords: modified wave operators
zbMATH Keywords: Hartree equation
zbMATH Keywords: asymptotic completeness
MaRDI profile type: Publication
full work available at URL: cpaa.2002.1.237
OpenAlex ID: W1978207407
DOI: 10.3934/CPAA.2002.1.237
description: scientific article; zbMATH DE number 1833242