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  1. Home
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  3. Defocusing Nonlinear Schrödinger Equations
  • Cited by 13
Publisher:
Cambridge University Press
Online publication date:
March 2019
Print publication year:
2019
Online ISBN:
9781108590518
DOI:
https://doi.org/10.1017/9781108590518
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
Series:
Cambridge Tracts in Mathematics (217)
Information

Book description

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.

Reviews

‘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 Source: MathSciNet

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