涡量和不可压缩流
作者：世界图书出版公司北京公司
出版时间： 2003年版
内容简介
涡量也许是湍流流动的最重要的因素。这本书的目的是要全面介绍了数学理论的涡和不可压缩流，范围从基本的介绍材料，以目前的研究课题。虽然对数学理论的内容中心，书中的许多地方展示调制解调器应用数学严格的数学理论，数值，渐近和定性的简化建模，物理现象之间的互动。有兴趣的读者可以看到这整个挂钩的共生互动的例子很多，尤其是在CHAPS，。4-9和13。作者希望，这种观点将是有趣的数学家以及其他科学家和工程师不可压缩流动的数学理论的兴趣。
目录
序言
第1章的注意事项
参考第1章
1为不可压缩流体涡动力学流动
1.1 Euler和Navier - Stokes方程
1.2 Euler和Navier - Stokes方程的对称群
1.3粒子轨迹
1.4涡度，一个变形矩阵，和一些基本的精确解
1.5简单的对流，拉伸涡和扩散的精确解
1.6一些显着的特点在理想流体的涡流
1.7在理想和粘性流体流动的守恒量
1.8不可压缩流和Hodge'的向量场分解Leray'的配方
1.9附录
第2章的注意事项
参考第2章
2 Euier和纳维Vorfidty流配方。 Stokes方程
2.1二维流动的涡流配方
2.2构建精确的二维Euler方程的稳态解的一般方法
2.3一些特殊的非平凡涡动力学三维流动
2.4三维流动的涡流配方
2.5配方粒子轨迹的积分微分方程的欧拉方程
第3章的注意事项
参考第3章
3 Euler和Navier - Stokes方程的能量方法
3.1能量方法：小学概念
3.2解决方案的地方，存在时间由能源方法
3.3积累的涡度和光滑解的存在性在全球范围内时间
3.4粘性Navier - Stokes方程的分裂算法
3.5第3章附录
第4章的注意事项
参考第4章
4存在和解决方案的唯一性粒子轨迹法的欧拉方程
4.1粘性解决方案的地方，存在时间
4.2全球实时光滑解的存在性和通过拉伸涡度积累之间的联系
4.3全球存在无涡流三维轴对称流动
4.4高等教育规律
4.5附录第4章
第5章的注意事项
参考第5章
5搜索三维Euler方程的奇异解
5.1在搜索奇异解的数学理论和数值计算之间的相互作用
5.2一个简单的一维模型的三维涡度方程
5.3在三维Euler方程的潜在形成奇异的2D模型
5.4潜在的奇异3D轴对称涡流流动
5.5的3D欧拉解决方案成为在有限时报债券奇异的
第6章的注意事项
参考第6章
6计算涡方法
6.1粘性剪切层紧张的随机涡方法
6.2二维粘性涡方法
6.3三维粘性涡方法
6.4粘性涡方法的收敛性
6.5计算性能的二维粘性涡方法基于一个简单的模型问题
6.6在二维的随机涡方法
6.7附录第6章
第7章的注意事项
参考第7章
7简体细长涡丝的渐近方程
7.1自感逼近，Hasimoto'的变换，非线性薛定谔方程
7.2自我伸展为单涡丝简体渐近方程
7.3交互并行涡丝 - 在平面上的点涡
7.4近于平行的涡丝互动的渐近方程
7.5数学和应用数学问题，关于渐近涡丝
第8章的注意事项
参考第8章
8日至初步Vorticlty在L 2D欧拉方程的弱解
8.1椭圆Vorticies
8.2涡度方程的弱大号解决方案
8.3涡的修补程序
8.4第8章的附录
第9章的注意事项
参考第9章
9涡表“，”弱“的解决方案和Euler方程的近似解序列
9.1在原始变量形式的欧拉方程的弱形式
9.2古典涡表和伯克霍夫Rott公式
9.3的Kelvin - Helmholtz不稳定性
9.4计算涡表
9.5振荡和浓度的发展
第10章的注意事项
参考第10章
10弱的解决方案和解决方案序列在两个方面
10.1近似解序列的Euler和Navier - Stokes方程
10.2 L1和LP 2D序列的收敛结果
第11章的注意事项
参考第11章
11二维Euler方程的涡初始数据手册中的浓度与弱解
11.1弱*和减少缺陷的措施
11.2与浓度的例子
11.3涡度的最大功能：衰变率和强收敛
11.4弱解涡初始数据手册中的杰出登录的存在性
第12章的注意事项
参考第12章
12 Hansdorff尺寸减少，振荡，和测量值的解决方案，在二维和三维的欧拉方程
12.1 Hausdorff维数减少
12.2近似解序列的振荡没有L1涡控制
12.3年轻的措施和测量值的欧拉方程的解决方案
12.4测量振荡和浓度值的解决方案
第13章的注意事项
参考第13章
13弗拉索夫泊松方程NS一个比喻的欧拉方程的弱解的研究
13.1之间的二维Euler方程和1D弗拉索夫泊松方程的比喻
13.2单组分1D弗拉索夫- Poisson方程
13.3双组分弗拉索夫泊松系统
指数
Preface
1 An Introduction to Vortex Dynamics for Incompressible Fluid Flows
1.1 The Euler and the Navier-Stokes Equations
1.2 Symmetry Groups for the Euler and the Navier-Stokes Equations
1.3 Particle Trajectories
1.4 The Vorticity, a Deformation Matrix, and Some Elementary Exact Solutions
1.5 Simple Exact Solutions with Convection, Vortex Stretching, and Diffusion
1.6 Some Remarkable Properties of the Vorticity in Ideal Fluid Flows
1.7 Conserved Quantities in Ideal and Viscous Fluid Flows
1.8 Leray''s Formulation of Incompressible Flows and Hodge''s Decomposition of Vector Fields
1.9 Appendix
Notes for Chapter 1
References for Chapter 1
2 The Vorfidty-Stream Formulation of the Euier and the Navier. Stokes Equations
2.1 The Vorticity-Stream Formulation for 2D Flows
2.2 A General Method for Constructing Exact Steady Solutions to the 2D Euler Equations
2.3 Some Special 3D Flows with Nontrivial Vortex Dynamics
2.4 The Vorticity-Stream Formulation for 3D Flows
2.5 Formulation of the Euler Equation as an Integrodifferential Equation for the Particle Trajectories
Notes for Chapter 2
References for Chapter 2
3 Energy Methods for the Euler and the Navier-Stokes Equations
3.1 Energy Methods: Elementary Concepts
3.2 Local-in-Time Existence of Solutions by Means of Energy Methods
3.3 Accumulation of Vorticity and the Existence of Smooth Solutions Globally in Time
3.4 Viscous-Splitting Algorithms for the Navier-Stokes Equation
3.5 Appendix for Chapter 3
Notes for Chapter 3
References for Chapter 3
4 The Particle-Trajectory Method for Existence and Uniqueness of Solutions to the Euler Equation
4.1 The Local-in-Time Existence of Inviscid Solutions
4.2 Link between Global-in-Time Existence of Smooth Solutions and the Accumulation of Vorticity through Stretching
4.3 Global Existence of 3D Axisymmetric Flows without Swirl
4.4 Higher Regularity
4.5 Appendixes for Chapter 4
Notes for Chapter 4
References for Chapter 4
5 The Search for Singular Solutions to the 3D Euler Equations
5.1 The Interplay between Mathematical Theory and Numerical Computations in the Search for Singular Solutions
5.2 A Simple 1D Model for the 3D Vorticity Equation
5.3 A 2D Model for Potential Singularity Formation in 3D Euler Equations
5.4 Potential Singularities in 3D Axisymmetric Flows with Swirl
5.5 Do the 3D Euler Solutions Become Singular in Finite Times Notes for Chapter 5
References for Chapter 5
6 Computational Vortex Methods
6.1 The Random-Vortex Method for Viscous Strained Shear Layers
6.2 2D Inviscid Vortex Methods
6.3 3D Inviscid-Vortex Methods
6.4 Convergence of Inviscid-Vortex Methods
6.5 Computational Performance of the 2D Inviscid-Vortex Method on a Simple Model Problem
6.6 The Random-Vortex Method in Two Dimensions
6.7 Appendix for Chapter 6
Notes for Chapter 6
References for Chapter 6
7 Simplified Asymptotic Equations for Slender Vortex Filaments
7.1 The Self-Induction Approximation, Hasimoto''s Transform, and the Nonlinear Schrodinger Equation
7.2 Simplified Asymptotic Equations with Self-Stretch for a Single Vortex Filament
7.3 Interacting Parallel Vortex Filaments - Point Vortices in the Plane
7.4 Asymptotic Equations for the Interaction of Nearly Parallel Vortex Filaments
7.5 Mathematical and Applied Mathematical Problems Regarding Asymptotic Vortex Filaments
Notes for Chapter 7
References for Chapter 7
8 Weak Solutions to the 2D Euler Equations with Initial Vorticlty in L
8.1 Elliptical Vorticies
8.2 Weak L Solutions to the Vorticity Equation
8.3 Vortex Patches
8.4 Appendix for Chapter 8
Notes for Chapter 8
References for Chapter 8
9 Introduction to Vortex Sheets, Weak Solutions, and Approximate-Solution Sequences for the Euler Equation
9.1 Weak Formulation of the Euler Equation in Primitive-Variable Form
9.2 Classical Vortex Sheets and the Birkhoff-Rott Equation
9.3 The Kelvin-Helmholtz Instability
9.4 Computing Vortex Sheets
9.5 The Development of Oscillations and Concentrations
Notes for Chapter 9
References for Chapter 9
10 Weak Solutions and Solution Sequences in Two Dimensions
10.1 Approximate-Solution Sequences for the Euler and the Navier-Stokes Equations
10.2 Convergence Results for 2D Sequences with L1 and Lp
Vorticity Control
Notes for Chapter 10
References for Chapter 10
11 The 2D Euler Equation: Concentrations and Weak Solutions with Vortex-Sheet Initial Data
11.1 Weak-* and Reduced Defect Measures
11.2 Examples with Concentration
11.3 The Vorticity Maximal Function: Decay Rates and Strong Convergence
11.4 Existence of Weak Solutions with Vortex-Sheet Initial Data of Distinguished Sign
Notes for Chapter 11
References for Chapter 11
12 Reduced Hansdorff Dimension, Oscillations, and Measure-Valued Solutions of the Euler Equations in Two and Three Dimensions
12.1 The Reduced Hausdorff Dimension
12.2 Oscillations for Approximate-Solution Sequences without L1 Vorticity Control
12.3 Young Measures and Measure-Valued Solutions of the Euler Equations
12.4 Measure-Valued Solutions with Oscillations and Concentrations
Notes for Chapter 12
References for Chapter 12
13 The Vlasov-Poisson Equations ns an Analogy to the Euler Equations for the Study of Weak Solutions
13.1 The Analogy between the 2D Euler Equations and the 1D Vlasov-Poisson Equations
13.2 The Single-Component 1D Vlasov-Poisson Equation
13.3 The Two-Component Vlasov-Poisson System
Note for Chapter 13
References for Chapter 13
Index
