非线性Schrödinger方程的全局解（影印版）

样章

作者：

J. Bourgain

定价：

99.00元

ISBN：

978-7-04-063100-5

版面字数：

300.00千字

开本：

16开

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

出版时间：

2025-02-14

物料号：

63100-00

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

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