Defocusing Nonlinear Schrödinger Equations
Defocusing Nonlinear Schrödinger Equations
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DOI：
10.1017/9781108590518
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
B. Dodson
中科院分区：
文献类型：
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作者：
B. Dodson
对幂型非线性薛定谔方程的研究，对其他色散偏微分方程和几何偏微分方程的研究具有重要的启示意义。它提出了重要的证明，从谐波分析，微局部分析，功能分析和拓扑的工具。这包括对Keel-Tao端点Strichartz估计的新证明，以及对径向、能量临界NLS的Bourgain结果的新证明。本文还详细介绍了能量临界和质量临界方程的散射结果。这本书是适合作为一个学期的基础课程，并作为一个有用的介绍非线性薛定谔方程为那些在谐波分析，泛函分析，偏微分方程的背景。
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.