Benjamin Dodson

Defocusing Nonlinear Schrodinger Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 28. März 2019
• Englisch
• ISBN-13: 9781108681674
• Artikelnr.: 56681350

Autorenporträt

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.

Inhaltsangabe

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.