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Strichartz Estimates and Applications to Semilinear Dispersive Equations

  • Hajer BahouriEmail author
  • Jean-Yves Chemin
  • Raphaël Danchin
Chapter
  • 4.5k Downloads
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 343)

Abstract

Chapter 8 is devoted to Strichartz estimates for dispersive equations with a focus on Schrödinger and wave equations. After proving a dispersive inequality (i.e., decay in time of the L norm in space) for these equations, we present, in a self-contained way, the celebrated TT argument based on a duality method and on bilinear estimates. Some examples of applications to semilinear Schrödinger and wave equations are given at the end of the chapter.

Keywords

Wave Equation Sobolev Embedding Cauchy Data Strichartz Estimate Fourier Integral Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hajer Bahouri
    • 1
    Email author
  • Jean-Yves Chemin
    • 2
  • Raphaël Danchin
    • 3
  1. 1.Départment de Mathématiques, Faculté des Sciences de Tunis, Campus UniversitaireUniversité de Tunis El ManarTunisTunisia
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  3. 3.Centre de Mathématiques, Faculté de Sciences et TechnologieUniversité Paris XII-Val de MarneCréteil CedexFrance

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