Defocusing Nonlinear Schrödinger Equations

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

Benjamin Dodson (Author)

9781108472081, Cambridge University Press

Hardback, published 28 March 2019

254 pages
23.5 x 15.6 x 1.8 cm, 0.48 kg

'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

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.

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.

Subject Areas: Differential calculus & equations [PBKJ], Functional analysis & transforms [PBKF]