非线性Schrödinger方程的全局解（影印版）

样章

作者：

J. Bourgain

定价：

99.00 元

版面字数：

300千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063100-5

物料号：

63100-00

出版时间：

2025-02-14

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

偏微分方程

暂无

目录
- 前辅文
- Introduction and summary
- I. An overview of results on the Cauchy problem for NLS
  - 1. Equations
  - 2. Wellposedness of the Cauchy problen
  - 3. Scattering results
  - 4. Estimates on the linear group
  - 5. Solving the Cauchy problem
  - 6. Derivative nonlinear Schrödinger equations
- II. Further comments
  - 1. Construction of blowup solutions for conformal NLS from the ground state
  - 2. Behaviour of higher Sobolev norms
  - 3. Fourier restriction theory beyond L2
  - 4. L2-concentration phenomenon
  - 5. The Schrödinger maximal function
  - 6. Derivative nonlinear Schrodinger equation
- III. 3D H1-critical defocusing NLS
  - 1. Consider 3D NLS
  - 2. Fix a time interval I=[0,T]
  - 3. Sketch of the argument
  - 4. A concentration property
  - 5. A version of Morawetz inequality
  - 6. Construction of an appropriate time interval
  - 7. Details on the perturbative analysis
  - 8. A variant of the method
- IV. Global wellposedness below energy norm
  - 1. Description of the method
  - 2. The example of the NLW
  - 3. The case of the nonlinear Schrödinger equation
  - 4. Symplectic capacities and symplectic Hilbert spaces
  - 5. Global wellposedness of the NLW (4.41)
- V. Nonlinear Schrödinger equation with periodic boundary conditions
  - 1. Introduction
  - 2. Results on the Cauchy problem
  - 3. Periodic Strichartz inequalities
  - 4. Sketch of proof of Theorems 2.1 and 2.7
  - 5. Invariant Gibbs measures (1D)
  - 6. Invarinat Gibbs measures (D>1)
  - 7. Invariant Gibbs measures (unbounded domains)
  - 8. Quasi-periodic solutions
- Appendix 1. Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
- Appendix 2. Zakharov systems
- References
- Index