Defocusing Nonlinear Schrödinger Equations

ISBN-13: 9781108472081 / Angielski / Twarda / 2019 / 254 str.

Benjamin Dodson (The Johns Hopkins Unive

Opis

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.

Recenzje

'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, MathSciNet

Spis treści

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.