Defocusing Nonlinear Schroedinger Equations

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.

Benjamin Dodson is Associate Professor in the Department of Mathematics at The Johns Hopkins University. His main research interests include partial differential equations and harmonic analysis.

'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