Dispersive Equations and Nonlinear Waves

Generalized Kortewegâ"de Vries, Nonlinear Schrodinger, Wave and Schrodinger Maps

By: Daniel Tataru, Monica Visan, Herbert Koch

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Paperback | 31 July 2014 | Edition Number 2014

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Paperback
328 Pages

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17.1 x 24.0 x 1.7

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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 Schrodinger 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 Schrodinger 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.

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