书目名称 | Dispersive Equations and Nonlinear Waves | 副标题 | Generalized Korteweg | 编辑 | Herbert Koch,Daniel Tataru,Monica Vişan | 视频video | | 概述 | 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.Intr | 丛书名称 | Oberwolfach Seminars | 图书封面 |  | 描述 | 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. | 出版日期 | Textbook 2014 | 关键词 | Fourier transform; dispersion; wave interaction; wave propagation; partial differential equations | 版次 | 1 | doi | https://doi.org/10.1007/978-3-0348-0736-4 | isbn_softcover | 978-3-0348-0735-7 | isbn_ebook | 978-3-0348-0736-4Series ISSN 1661-237X Series E-ISSN 2296-5041 | issn_series | 1661-237X | copyright | Springer Basel 2014 |
The information of publication is updating
|
|