《可壓縮流與歐拉方程(英文版)》主要考慮三維空間中，其初值在單位球面外為常值的任意狀態方程的經典可壓縮歐拉方程。當初值與常狀態差別適當小時，我們建立的定理可以給出關於解的完整描述。特別地，解的定義域的邊界包含一個奇異部分，在那裡波前的密度將會趨向於無窮大，從而激波形成。在《可壓縮流與歐拉方程(英文版)》中，我們採用幾何化方法得到了關於這個奇異部分的完整的幾何描述以及解在這部分性態的詳細分析，其核心概念是聲學時空流形。與相關領域中其他數學家的工作相比，《可壓縮流與歐拉方程(英文版)》的結果相對完整並且具有一般性。與《可壓縮流與歐拉方程(英文版)》第一作者之前的一個關於相對論流體的工作相比，《可壓縮流與歐拉方程(英文版)》不僅給出了更簡單且自成體系的證明，而且還把某些結論做得更優。同時《可壓縮流與歐拉方程(英文版)》還詳細解釋了證明方法中的主要思想，討論了只在非相對論情形出現的一些幾何上的性質。
基本介紹
- 書名：可壓縮流與歐拉方程
- 作者：克里斯托多羅 (Demetrios Christodoulou) 繆爽
- 出版社：高等教育出版社
- 頁數：648頁
- 開本：16
- 外文名：Compressible Flow and Euler's Equations
- 類型：英語與其他外語
- 出版日期：2014年8月1日
- 語種：簡體中文, 英語
- ISBN：9787040400991
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《可壓縮流與歐拉方程(英文版)》可供從事偏微分方程研究，特別是從事流體動力學研究的數學家參者。
作者簡介
作者：（美國）克里斯托多羅（Demetrios Christodoulou） 譯者：繆爽
圖書目錄
Compressible Flow and Non—linear Wave Equations
1.1 Euler's Equations
1.2 Irrotational Flow and the Nonlinear Wave Equation
1.3 The Equation of Variations and the Acoustical Metric
1.4 The Fundamental Variations
2 The Basic Geometric Construction
2.1 Null Foliation Associated with the Acoustical Metric
2.1.1 Galilean Spacetime
2.1.2 Null Foliation and Acoustical Coordinates
2.2 A Geometric Interpretation for Function H
3 The Acoustical Structure Equations
3.1 The Acoustical Structure Equations ：
3.2 The Derivatives of the Rectangular Components of L and T
The Acoustical Curvature
4.1 Expressions for Curvature Tensor
4.2 Regularity for the Acoustical Structure Equations as # ～ 0
4.3 A Remark
5 The Fundamental Energy Estimate
5.1 Bootstrap Assumptions. Statement of the Theorem
5.2 The Multiplier Fields K0 and K1. The Associated Energy—Momentum Density Vectorfields
5.3 The Error Integrals
5.4 The Estimates for the Error Integrals
5.5 Treatment of the Integral Inequalities Depending on t and u.
Completion of the Proof
6 Construction of Commutation Vectorfields
6.1 Commutation Vectorfields and Their Deformation Tensors
6.2 Preliminary Estimates for the Deformation Tensors
7 Outline of the Derived Estimates of Each Order
8 Regularization of the Propagation Equation for ～trx.Estimates for the Top Order Angular Derivatives of X
9 Regularization of the Propagation Equation for u.Estimates for the Top Order Spatial Derivatives of u
10 Control of the Angular Derivatives of the First Derivatives of the xi. Assumptions and Estimates in Regard to X
11 Control of the Spatial Derivatives of the First Derivatives of the xi. Assumptions and Estimates in Regard to u
……
References
1.1 Euler's Equations
1.2 Irrotational Flow and the Nonlinear Wave Equation
1.3 The Equation of Variations and the Acoustical Metric
1.4 The Fundamental Variations
2 The Basic Geometric Construction
2.1 Null Foliation Associated with the Acoustical Metric
2.1.1 Galilean Spacetime
2.1.2 Null Foliation and Acoustical Coordinates
2.2 A Geometric Interpretation for Function H
3 The Acoustical Structure Equations
3.1 The Acoustical Structure Equations ：
3.2 The Derivatives of the Rectangular Components of L and T
The Acoustical Curvature
4.1 Expressions for Curvature Tensor
4.2 Regularity for the Acoustical Structure Equations as # ～ 0
4.3 A Remark
5 The Fundamental Energy Estimate
5.1 Bootstrap Assumptions. Statement of the Theorem
5.2 The Multiplier Fields K0 and K1. The Associated Energy—Momentum Density Vectorfields
5.3 The Error Integrals
5.4 The Estimates for the Error Integrals
5.5 Treatment of the Integral Inequalities Depending on t and u.
Completion of the Proof
6 Construction of Commutation Vectorfields
6.1 Commutation Vectorfields and Their Deformation Tensors
6.2 Preliminary Estimates for the Deformation Tensors
7 Outline of the Derived Estimates of Each Order
8 Regularization of the Propagation Equation for ～trx.Estimates for the Top Order Angular Derivatives of X
9 Regularization of the Propagation Equation for u.Estimates for the Top Order Spatial Derivatives of u
10 Control of the Angular Derivatives of the First Derivatives of the xi. Assumptions and Estimates in Regard to X
11 Control of the Spatial Derivatives of the First Derivatives of the xi. Assumptions and Estimates in Regard to u
……
References
