manuscripta mathematica

, Volume 61, Issue 4, pp 477–494

The Cauchy problem for the nonlinear Schrödinger equation in H1

  • Thierry Cazenave
  • Fred B. Weissler

DOI: 10.1007/BF01258601

Cite this article as:
Cazenave, T. & Weissler, F.B. Manuscripta Math (1988) 61: 477. doi:10.1007/BF01258601


We consider the initial value problem for the nonlinear Schrödinger equation in H1(Rn). We establish local existence and uniqueness for a wide class of subcritical nonlinearities. The proofs make use of a truncation argument, space-time integrability properties of the linear equation, anda priori estimates derived from the conservation of energy. In particular, we do not need any differentiability property of the nonlinearity with respect to x.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Thierry Cazenave
    • 1
  • Fred B. Weissler
    • 1
    • 2
  1. 1.Analyse NumériqueUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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