Defocusing nonlinear Schrödinger equations

Type Book

Rate 0.0 /5

This study of Schrödinger 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 …

Details

Files

Reviews

Download

Title Statements

Full title :Defocusing nonlinear Schrödinger equations / Benjamin Dodson, The Johns Hopkins University.

Summary

This study of Schrödinger 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 Schrödinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.

Edition Statements

Publication Date:©2019

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, United Kingdom
Language:eng
Publication Date:©2019

The Physical Object

Description:xii, 242 pages ; : 24 cm.

Edition Identifiers

ISBN:1108472087, 9781108472081
oclc:on1074292311
LC Classification:QC174.26.W28
Dewey Decimal:530.12/4

A first look at the mass-critical problem -- The cubic NLS in dimensions three and four -- The energy-critical problem in higher dimensions -- Mass-critical NLS problem in higher dimensions -- Low-dimensional well-posedness results.

Subjects