了得網自然科學_可壓縮流與歐拉方程（英文版）(Compressible Flow and Euler's

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可壓縮流與歐拉方程（英文版）(Compressible Flow and Euler's
該商品所屬分類：自然科學 -> 力學
【市場價】	635-920元
【優惠價】	397-575元
【作者】	美克裡斯托多羅，繆爽　著
【所屬類別】	圖書自然科學力學
【出版社】	高等教育出版社
【ISBN】	9787040400984
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內容介紹

開本：16開

紙張：膠版紙

包裝：精裝

是否套裝：否

國際標準書號ISBN：9787040400984

作者：(美)克裡斯托多羅，繆爽著

出版社：高等教育出版社

出版時間：2014年08月

內容簡介

本書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。在本書中，我們采用幾何化方法，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。

1Compressible Flow and Non-linear Wave Equations
1.1Euler's Equations
1.2Irrotational Flow and the Nonlinear Wave Equation
1.3The Equation of Variations and the Acoustical Metric
1.4The Fundamental Variations
2The Basic Geometric Construction
2.1Null Foliation Associated with the Acoustical Metric
2.1.1Galilean Spacetime
2.1.2Null Foliation and Acoustical Coordinates
2.2A Geometric Interpretation for Function H
3The Acoustical Structure Equations
3.1The Acoustical Structure Equations
3.2The Derivatives of the Rectangular Components of L and T
4The Acoustical Curvature1Compressible Flow and Non-linear Wave Equations

1.1Euler's Equations

1.2Irrotational Flow and the Nonlinear Wave Equation

1.3The Equation of Variations and the Acoustical Metric

1.4The Fundamental Variations

2The Basic Geometric Construction

2.1Null Foliation Associated with the Acoustical Metric

2.1.1Galilean Spacetime

2.1.2Null Foliation and Acoustical Coordinates

2.2A Geometric Interpretation for Function H

3The Acoustical Structure Equations

3.1The Acoustical Structure Equations

3.2The Derivatives of the Rectangular Components of L and T

4The Acoustical Curvature

4.1Expressions for Curvature Tensor

4.2Regularity for the Acoustical Structure Equations as μ → 0

4.3A Remark

5The Fundamental Energy Estimate

5.1Bootstrap Assumptions. Statement of the Theorem

5.2The Multiplier Fields K0 and K1. The Associated Energy-Momentum Density Vectorfields

5.3The Error Integrals

5.4The Estimates for the Error Integrals

5.5Treatment of the Integral Inequalities Depending on t and u.

Completion of the Proof

6Construction of Commutation Vectorfields

6.1Commutation Vectorfields and Their Deformation Tensors

6.2Preliminary Estimates for the Deformation Tensors

7Outline of the Derived Estimates of Each Order

7.1The Inhomogeneous Wave Equations for the Higher Order Variations. The Recursion Formula for the Source Functions

7.2The First Term in ρn

7.3The Estimates of the Contribution of the First Term in ρn to the Error Integrals

8Regularization of the Propagation Equation for □trX. Estimates for the Top Order Angular Derivatives of X

8.1Preliminary

8.1.1Regularization of The Propagation Equation

8.1.2Propagation Equations for Higher Order Angular Derivatives

8.1.3Elliptic Theory on St,u

8.1.4Preliminary Estimates for the Solutions of the Propagation Equations

8.2Crucial Lemmas Concerning the Behavior of μ

8.3The Actual Estimates for the Solutions of the Propagation Equations

9 Regularization of the Propagation Equation for □μ.

Estimates for the Top Order Spatial Derivatives of μ

9.1Regularization of the Propagation Equation

9.2Propagation Equations for the Higher Order Spatial Derivatives

9.3Elliptic Theory on St,u

9.4The Estimates for the Solutions of the Propagation Equations

10Control of the Angular Derivatives of the First Derivatives of

the xi. Assumptions and Estimates in Regard to X

10.1 Preliminary

10.2 Estimates for yi

10.2.1 L∞ Estimates for Rik ... .Ri1yj

10.2.2 L2 Estimates for Rik... Pi1yj

10.3 Bounds for the quantities Ql and Pl

10.3.1 Estimates for Ql

10.3.2 Estimates for Pl

11Control of the Spatial Derivatives of the First Derivatives of

the xi. Assumptions and Estimates in Regard to μ

11.1 Estimates for TTi

11.1.1 Basic Lemmas

11.1.2 L∞ Estimates for TTi

11.1.3 L2 Estimates for TTi

11.2 Bounds for Quantities Q'm,l and P'm,l

11.2.1 Bounds for Q'm,l

11.2.2 Bounds for P'm,l

12Recovery of the Acoustical Assumptions

Estimates for Up to the Next to the Top Order Angular

Derivatives of X and Spatial Derivatives of μ

12.1Estimates for λi, y', yi and r. Establishing the Hypothesis H0

12.2The Coercivity Hypothesis H1, H2 and H2'. Estimates for X'

12.3Estimates for Higher Order Derivatives of X' and μ

13Derivation of the Basic Properties of μ

14The Error Estimates Involving the Top Order Spatial

Derivatives of the Acoustical Entities

14.1 The Error Terms Involving the Top Order Spatial

Derivatives of the Acoustical Entities

14.2 The Borderline Error Integrals

14.3 Assumption J

14.4 The Borderline Estimates Associated to K0

14.4.1 Estimates for the Contribution of (14.56)

14.4.2 Estimates for the Contribution of (14.57)

14.5 The Borderline Estimates Associated to K1

14.5.1 Estimates for the Contribution of (14.56)

14.5.2 Estimates for the Contribution of (14.57)

15The Top Order Energy Estimates

15.1 Estimates Associated to K1

15.2 Estimates Associated to K0

16The Descent Scheme

17The Isoperimetric Inequality. Recovery of Assumption J.

Recovery of the Bootstrap Assumption. Proof of the Main

Theorem

17.1 Recovery of J--Preliminary

17.2 The Isoperimetric Inequality

17.3 Recovery of J--Completion

17.4 Recovery of the Final Bootstrap Assumption

17.5 Completion of the Proof of the Main Theorem

18Sufficient Conditions on the Initial Data for the Formation of a Shock in the Evolution

19The Structure of the Boundary of the Domain of the Maximal Solution

19.1 Nature of Singular Hypersurface in Acoustical Differential Structure

19.1.1 Preliminary

19.1.2 Intrinsic View Point

19.1.3 Invariant Curves

19.1.4 Extrinsic View Point

19.2 The Trichotomy Theorem for Past Null Geodesics Ending at Singular Boundary

19.2.1 Hamiltonian Flow

19.2.2 Asymptotic Behavior

19.3 Transformation of Coordinates

19.4 How H Looks Like in Rectangular Coordinates in Galilean Spacetime

References

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