Defocusing Nonlinear Schrödinger Equations

Erscheinungsjahr 2019
ISBN: 978-1-108-47208-1
Verlag: Cambridge University Press

Buch, Englisch, Band 217, 256 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 571 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Dodson, Benjamin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.

Über Autor(innen)

Dodson, Benjamin
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.