Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We consider the Cauchy problem for the cubic nonlinear Schrödinger equation {equation presented} The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u0 ∈ Hα∩H0,α with α > 1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u0 ∈ H2∩H0,2. Also we find the large-time asymptotics of solutions.

Original languageEnglish
Pages (from-to)801-828
Number of pages28
JournalDifferential and Integral Equations
Volume24
Issue number9-10
Publication statusPublished - 2011 Sep
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces'. Together they form a unique fingerprint.

Cite this