Small solutions to nonlinear Schrödinger equations in the Sobolev spaces

M. Nakamura*, T. Ozawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The local and global well-posedness for the Cauchy problem for a class of nonlinear Schrödinger equations is studied. The global well-posedness of the problem is proved in the Sobolev space Hs = Hs(Rn) of fractional order s > n/2 under the following assumptions. (1) Concerning the Cauchy data φ ∈ Hs: ∥φ; L2∥ is relatively small with respect to ∥φ; Hσ∥ for any fixed σ with n/2 < σ ≤ s. (2) Concerning the nonlinearity f: f(u) behaves as a conformal power u1+4/n near zero and has an arbitrary growth rate at infinity.

Original languageEnglish
Pages (from-to)305-329
Number of pages25
JournalJournal d'Analyse Mathematique
Publication statusPublished - 2000 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • General Mathematics


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