Dispersive Equations and Nonlinear Waves: Generalized Korteweg?de Vries, Nonlinear Schr?dinger, Wave and Schr?dinger Maps (Oberwolfach Seminars, 45)

Visan Monica Vi?an Monica Tataru Daniel Koch Herbert

ISBN 10: 303480735X / ISBN 13: 9783034807357

Published by Springer, 2014

About this Item

Print on Demand pp. xii + 312.

Seller Inventory # 94564390

Bibliographic Details

• Title: Dispersive Equations and Nonlinear Waves: Generalized Korteweg?de Vries, Nonlinear Schr?dinger, Wave and Schr?dinger Maps (Oberwolfach Seminars, 45)
• Publisher: Springer
• Publication Date: 2014
• Language: English
• ISBN 10: 303480735X
• ISBN 13: 9783034807357
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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 Author

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.