Journal d’Analyse Mathématique

, Volume 81, Issue 1, pp 305–329 | Cite as

Small solutions to nonlinear Schrödinger equations in the Sobolev spaces

  • M. Nakamura
  • T. Ozawa


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 spaceH s=Hs(R n) of fractional orders>n/2 under the following assumptions. (1) Concerning the Cauchy data ϕ∈H s: ‖ϕ;L 2‖ is relatively small with respect to ‖ϕ;H σ‖ for any fixed σ withn/2<σ≤s. (2) Concerning the nonlinearityf: f(u) behaves as a conformal poweru 1+4/n near zero and has an arbitrary growth rate at infinity.


Cauchy Problem Sobolev Space Unique Fixed Point Admissible Pair Cauchy Data 
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Copyright information

© Hebrew University of Jerusalem 2000

Authors and Affiliations

  • M. Nakamura
    • 1
  • T. Ozawa
    • 2
  1. 1.Graduate School of Information Sciences (GSIS)Tohoku UniversitySendaiJapan
  2. 2.Department of MathematicsHokkaido UniversitySapporoJapan

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