Defocusing Nonlinear Schroedinger Equations
Published on 20. March 2019
256 pages
978-1-108-68167-4 (ISBN)
Description
This study of Schroedinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel-Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schroedinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.
Reviews / Votes
'This book is an excellent introduction to the energy-critical and mass critical problems and is recommended to researchers and graduate students as a guide to advanced methods in nonlinear partial differential equations.' Tohru Ozawa, MathSciNetMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
1,78 MB
ISBN-13
978-1-108-68167-4 (9781108681674)
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Schweitzer Classification
Other editions
Additional editions
Benjamin Dodson
Defocusing Nonlinear Schroedinger Equations
Book
03/2019
Cambridge University Press
€153.60
Shipment within 15-20 days
Person
Content
Preface; 1. A first look at the mass-critical problem; 2. The cubic NLS in dimensions three and four; 3. The energy-critical problem in higher dimensions; 4. The mass-critical NLS problem in higher dimensions; 5. Low dimensional well-posedness results; References; Index.
