Critical nonlinear Schrödinger equations in higher space dimensions

Nakao Hayashi, Chunhua Li, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study the critical nonlinear Schrödinger equations iδtu +1/2Δu = λ|u|2/nu; (t; x) ∈ R+ × Rn; in space dimensions n ≥ 4; where λ ∈ R. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.

Original languageEnglish
Pages (from-to)1475-1492
Number of pages18
JournalJournal of the Mathematical Society of Japan
Volume70
Issue number4
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • Critical NLS equations
  • Higher space dimensions
  • Large time asymptotics

ASJC Scopus subject areas

  • Mathematics(all)

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