Small solutions to nonlinear Schrödinger equations in the Sobolev spaces

M. Nakamura, Tohru Ozawa

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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
Volume81
Publication statusPublished - 2000
Externally publishedYes

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Small Solutions
Global Well-posedness
Sobolev Spaces
Nonlinear Equations
Fractional Order
Cauchy
Cauchy Problem
Infinity
Nonlinearity
Zero
Arbitrary
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Small solutions to nonlinear Schrödinger equations in the Sobolev spaces. / Nakamura, M.; Ozawa, Tohru.

In: Journal d'Analyse Mathematique, Vol. 81, 2000, p. 305-329.

Research output: Contribution to journalArticle

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