版權資訊
頁 數： 545
開 本： 16
紙 張： 膠版紙
I S B N ： 9787506265539
包 裝： 平裝
所屬分類： 圖書 >> 工業技術 >> 一般工業技術
定價：￥98.00
內容簡介
Vorticity is perhaps the most important facet of turbulent fluid flows. This book is intended to be a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. Although the contents center on mathematical theory, many parts of the book showcase a modem applied mathematics interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The interested reader can see many examples of this symbiotic interaction throughout the hook, especially in Chaps. 4-9 and 13. The authors hope that this point of view will be interesting to mathematicians as well as other scientists and engineers with interest in the mathematical theory of incompressible flows.
目錄
序言
第1章的注意事項
參考第1章
1為不可壓縮流體渦動力學流動
1.1 Euler和Navier - Stokes方程
1.2 Euler和Navier - Stokes方程的對稱群
1.3粒子軌跡
1.4渦度，一個變形矩陣，和一些基本的精確解
1.5簡單的對流，拉伸渦和擴散的精確解
1.6一些顯著的特點在理想流體的渦流
1.7在理想和粘性流體流動的守恆量
1.8不可壓縮流和Hodge'的向量場分解Leray'的配方
1.9附錄
第2章的注意事項
參考第2章
2 Euier和納維Vorfidty流配方。 Stokes方程
2.1二維流動的渦流配方
2.2構建精確的二維Euler方程的穩態解的一般方法
2.3一些特殊的非平凡渦動力學三維流動
2.4三維流動的渦流配方
2.5配方粒子軌跡的積分微分方程的歐拉方程
第3章的注意事項
參考第3章
3 Euler和Navier - Stokes方程的能量方法
3.1能量方法：國小概念
3.2解決方案的地方，存在時間由能源方法
3.3積累的渦度和光滑解的存在性在全球範圍內時間
3.4粘性Navier - Stokes方程的分裂算法
3.5第3章附錄
第4章的注意事項
參考第4章
4存在和解決方案的唯一性粒子軌跡法的歐拉方程
4.1粘性解決方案的地方，存在時間
4.2全球實時光滑解的存在性和通過拉伸渦度積累之間的聯繫
4.3全球存在無渦流三維軸對稱流動
4.4高等教育規律
4.5附錄第4章
第5章的注意事項
參考第5章
5搜尋三維Euler方程的奇異解
5.1在搜尋奇異解的數學理論和數值計算之間的相互作用
5.2一個簡單的一維模型的三維渦度方程
5.3在三維Euler方程的潛在形成奇異的2D模型
5.4潛在的奇異3D軸對稱渦流流動
5.5的3D歐拉解決方案成為在有限時報債券奇異的
第6章的注意事項
參考第6章
6計算渦方法
6.1粘性剪下層緊張的隨機渦方法
6.2二維粘性渦方法
6.3三維粘性渦方法
6.4粘性渦方法的收斂性
6.5計算性能的二維粘性渦方法基於一個簡單的模型問題
6.6在二維的隨機渦方法
6.7附錄第6章
第7章的注意事項
參考第7章
7簡體細長渦絲的漸近方程
7.1自感逼近，Hasimoto'的變換，非線性薛丁格方程
7.2自我伸展為單渦絲簡體漸近方程
7.3互動並行渦絲 - 在平面上的點渦
7.4近於平行的渦絲互動的漸近方程
7.5數學和套用數學問題，關於漸近渦絲
第8章的注意事項
參考第8章
8日至初步Vorticlty在L 2D歐拉方程的弱解
8.1橢圓Vorticies
8.2渦度方程的弱大號解決方案
8.3渦的修補程式
8.4第8章的附錄
第9章的注意事項
參考第9章
9渦表“，”弱“的解決方案和Euler方程的近似解序列
9.1在原始變數形式的歐拉方程的弱形式
9.2古典渦表和伯克霍夫Rott公式
9.3的Kelvin - Helmholtz不穩定性
9.4計算渦表
9.5振盪和濃度的發展
第10章的注意事項
參考第10章
10弱的解決方案和解決方案序列在兩個方面
10.1近似解序列的Euler和Navier - Stokes方程
10.2 L1和LP 2D序列的收斂結果
第11章的注意事項
參考第11章
11二維Euler方程的渦初始數據手冊中的濃度與弱解
11.1弱*和減少缺陷的措施
11.2與濃度的例子
11.3渦度的最大功能：衰變率和強收斂
11.4弱解渦初始數據手冊中的傑出登錄的存在性
第12章的注意事項
參考第12章
12 Hansdorff尺寸減少，振盪，和測量值的解決方案，在二維和三維的歐拉方程
12.1 Hausdorff維數減少
12.2近似解序列的振盪沒有L1渦控制
12.3年輕的措施和測量值的歐拉方程的解決方案
12.4測量振盪和濃度值的解決方案
第13章的注意事項
參考第13章
13弗拉索夫泊松方程NS一個比喻的歐拉方程的弱解的研究
13.1之間的二維Euler方程和1D弗拉索夫泊松方程的比喻
13.2單組分1D弗拉索夫- Poisson方程
13.3雙組分弗拉索夫泊松系統
指數
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
