Oberwolfach Seminars

Dispersive Equations and Nonlinear Waves

Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps

Authors: Koch, Herbert, Tataru, Daniel, Visan, Monica

  • Exposition of central ideas in dispersive equations
  • Basic techniques and function spaces
  • Coherent introduction to induction on energy, minimal blow up solutions and interaction Morawetz estimates
  • Introduction to gauge transform, choice of functions spaces, and control of interacting waves
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eBook $39.99
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  • ISBN 978-3-0348-0736-4
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Softcover $49.99
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  • ISBN 978-3-0348-0735-7
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Rent the ebook  
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About this Textbook

The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.​

About the authors

Herbert Koch has been a professor at the University of Bonn, Germany since 2006, Daniel Tataru at the University of California in Berkeley, USA, since 2001 and Monica Vişan is an associate professor at UCLA, USA.

Table of contents (25 chapters)

  • Introduction

    Koch, Herbert (et al.)

    Pages 3-3

  • Stationary phase and dispersive estimates

    Koch, Herbert (et al.)

    Pages 5-22

  • Strichartz estimates and small data for the nonlinear Schrödinger equation

    Koch, Herbert (et al.)

    Pages 23-39

  • Functions of bounded p-variation

    Koch, Herbert (et al.)

    Pages 41-71

  • Convolution of measures on hypersurfaces, bilinear estimates, and local smoothing

    Koch, Herbert (et al.)

    Pages 73-85

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-0348-0736-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-0348-0735-7
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Dispersive Equations and Nonlinear Waves
Book Subtitle
Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps
Authors
Series Title
Oberwolfach Seminars
Series Volume
45
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0736-4
DOI
10.1007/978-3-0348-0736-4
Softcover ISBN
978-3-0348-0735-7
Series ISSN
1661-237X
Edition Number
1
Number of Pages
XII, 312
Number of Illustrations and Tables
1 b/w illustrations
Topics