图书信息
图书目录
非线性Schrödinger方程的全局解（影印版）
暂无简介
作者：
J. Bourgain
定价：
99.00元
出版时间：
2025-02-14
ISBN：
978-7-04-063100-5
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
重点项目：
暂无
版面字数：
300.00千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
