Fourier Analysis and Nonlinear Partial Differential Equations

  • Hajer Bahouri
  • Jean-Yves Chemin
  • Raphaël Danchin

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 343)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 1-50
  3. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 51-121
  4. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 123-167
  5. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 169-202
  6. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 203-243
  7. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 245-289
  8. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 291-333
  9. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 335-387
  10. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 389-428
  11. Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
    Pages 429-496
  12. Back Matter
    Pages 497-523

About this book

Introduction

In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations.  It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity.

It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.

Keywords

35Q35, 76N10, 76D05, 35Q31, 35Q30 Fourier analysis Littlewood-Paley theory estimates partial differential equations

Authors and affiliations

  • Hajer Bahouri
    • 1
  • Jean-Yves Chemin
    • 2
  • Raphaël Danchin
    • 3
  1. 1., Départment de MathématiquesUniversité de Tunis El ManarTunisTunisia
  2. 2., Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  3. 3., Centre de MathématiquesUniversité Paris XII - Val de MarneCréteil CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16830-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-16829-1
  • Online ISBN 978-3-642-16830-7
  • Series Print ISSN 0072-7830
  • About this book