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Defocusing Nonlinear Schrödinger Equations: Cambridge Tracts in Mathematics, cartea 217

Autor Benjamin Dodson
en Limba Engleză Hardback – 28 mar 2019
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.
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Specificații

ISBN-13: 9781108472081
ISBN-10: 1108472087
Pagini: 254
Dimensiuni: 156 x 235 x 18 mm
Greutate: 0.45 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'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

Notă biografică


Descriere

Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schrödinger equations.