Defocusing nonlinear Schrödinger equations / Benjamin Dodson.

Format:

Book

Author/Creator:

Dodson, Benjamin, 1983- author.

Series:

Cambridge tracts in mathematics ; 217.

Cambridge tracts in mathematics ; 217

Language:

English

Subjects (All):

Gross-Pitaevskii equations.

Schrödinger equation.

Differential equations, Nonlinear.

Physical Description:

1 online resource (xii, 242 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2019.

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 22 Mar 2019).

Includes bibliographical references and index.

Other Format:

Print version: Dodson, Benjamin, 1983- author. Defocusing nonlinear Schrödinger equations

ISBN:

9781108590518

9781108681674

1108681670

1108590519