Defocusing Nonlinear Schr?dinger Equations [Hardcover]

Explores Schr?dinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schr?dinger equations.This study of the nonlinear Schr?dinger equation 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. Suitable for use in a one-semester course.This study of the nonlinear Schr?dinger equation 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. Suitable for use in a one-semester course.This study of Schr?dinger 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 KeelTao 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 Schr?dinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.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.This book is an excellent introduction to the energy-critical and mass critical problems andlsl