Critical nonlinear Schrödinger equations with data in homogeneous weighted L2 spaces

Chunhua Li, Nakao Hayashi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We consider the initial value problem for nonlinear Schrödinger equations with the critical nonlinearities λ1|u|2/nu, where Imλ1≤0, when the space dimension n=1, 2. We prove the global existence of small solutions in homogeneous weighted L2(Rn) spaces. It is shown that the small solutions decay uniformly like t-n/2 for t>1 if Imλ1=0. The higher uniform time decay rates t-n2(logt)-n2 for t>1 are obtained if Imλ1<0.

Original languageEnglish
Pages (from-to)1214-1234
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume419
Issue number2
DOIs
Publication statusPublished - 2014 Nov 15
Externally publishedYes

Keywords

  • Critical nonlinearities
  • Nonlinear Schrödinger equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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