Defocusing nonlinear Schrödinger equations
著者
書誌事項
Defocusing nonlinear Schrödinger equations
（Cambridge tracts in mathematics, 217）
Cambridge University Press, 2019
- : hardback
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注記
Includes bibliographical references and (p. 236-240) index
内容説明・目次
内容説明
This study of Schroedinger 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 Schroedinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.
目次
- 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.
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