Dispersive Equations and Nonlinear Waves: Generalized Korteweg-de Vries, Nonlinear Schringer, Wave and Schringer Maps (Paperback) (ISBN-13: 9783034807357)

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 Schr dinger 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 Schr dinger 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.​

Author: Herbert Koch, Daniel Tataru, Monica Vişan
ISBN-10: 303480735X
ISBN-13: 9783034807357
Publisher: Birkhauser
Language: English
Published: 07/31/2014
Pages: 312
Format: Paperback
Weight: 1.25lbs
Size: 9.40h x 6.60w x 0.70d