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可压缩流与欧拉方程 英文版 Compressible Flow and Euler's EquationsPDF|Epub|txt|kindle电子书版本网盘下载
- DemetriosChristodoulou，Shuan 著
- 出版社： 北京：高等教育出版社
- ISBN：9787040400984
- 出版时间：2014
- 标注页数：582页
- 文件大小：59MB
- 文件页数：602页
- 主题词：可压缩流－英文；欧拉方程－英文
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图书目录
1 Compressible Flow and Non-linear Wave Equations1
1.1 Euler's Equations1
1.2 Irrotational Flow and the Nonlinear Wave Equation2
1.3 The Equation of Variations and the Acoustical Metric5
1.4 The Fundamental Variations6
2 The Basic Geometric Construction11
2.1 Null Foliation Associated with the Acoustical Metric11
2.1.1 Galilean Spacetime11
2.1.2 Null Foliation and Acoustical Coordinates12
2.2 A Geometric Interpretation for Function H19
3 The Acoustical Structure Equations21
3.1 The Acoustical Structure Equations21
3.2 The Derivatives of the Rectangular Components of L and ？33
4 The Acoustical Curvature39
4.1 Expressions for Curvature Tensor39
4.2 Regularity for the Acoustical Structure Equations asμ→042
4.3 A Remark45
5 The Fundamental Energy Estimate47
5.1 Bootstrap Assumptions.Statement of the Theorem47
5.2 The Multiplier Fields K0 and K1.The Associated Energy-Momentum Density Vectorfields50
5.3 The Error Integrals60
5.4 The Estimates for the Error Integrals63
5.5 Treatment of the Integral Inequalities Depending on t and u.Completion of the Proof76
6 Construction of Commutation Vectorfields83
6.1 Commutation Vectorfields and Their Deformation Tensors83
6.2 Preliminary Estimates for the Deformation Tensors88
7 Outline of the Derived Estimates of Each Order101
7.1 The Inhomogeneous Wave Equations for the Higher Order Variations.The Recursion Formula for the Source Functions101
7.2 The First Term in ？n104
7.3 The Estimates of the Contribution of the First Term in ？n to the Error Integrals109
8 Regularization of the Propagation Equation for ？trx.Estimates for the Top Order Angular Derivatives of x129
8.1 Preliminary129
8.1.1 Regularization of The Propagation Equation129
8.1.2 Propagation Equations for Higher Order Angular Derivatives133
8.1.3 Elliptic Theory on St,u143
8.1.4 Preliminary Estimates for the Solutions of the Propagation Equations151
8.2 Crucial Lemmas Concerning the Behavior of μ155
8.3 The Actual Estimates for the Solutions of the Propagation Equations174
9 Regularization of the Propagation Equation for ？μ.Estimates for the Top Order Spatial Derivatives of μ185
9.1 Regularization of the Propagation Equation185
9.2 Propagation Equations for the Higher Order Spatial Derivatives191
9.3 Elliptic Theory on St,u202
9.4 The Estimates for the Solutions of the Propagation Equations214
10 Control of the Angular Derivatives of the First Derivatives of the xi.Assumptions and Estimates in Regard to x227
10.1 Preliminary227
10.2 Estimates for yi238
10.2.1 L∞ Estimates for Rik…Ri1yj239
10.2.2 L2 Estimates for Rik…Ri1yj242
10.3 Bounds for the quantities Ql and Pl251
10.3.1 Estimates for Ql251
10.3.2 Estimates for Pl262
11 Control of the Spatial Derivatives of the First Derivatives of the xi.Assumptions and Estimates in Regard to μ269
11.1 Estimates for T？i269
11.1.1 Basic Lemmas269
11.1.2 L∞ Estimates for T？i287
11.1.3 L2 Estimates for T？i293
11.2Bounds for Quantities Q′m,l and P′m,l305
11.2.1 Bounds for Q′m,l306
11.2.2 Bounds for P′m,l316
12 Recovery of the Acoustical Assumptions.Estimates for Up to the Next to the Top Order Angular Derivatives of x and Spatial Derivatives ofμ327
12.1 Estimates for λi,y′i,yi and r.Establishing the Hypothesis HO327
12.2 The Coercivity Hypothesis H1,H2 and H2′.Estimates for x′332
12.3 Estimates for Higher Order Derivatives of x′and μ351
13 Derivation of the Basic Properties of μ381
14 The Error Estimates Involving the Top Order Spatial Derivatives of the Acoustical Entities397
14.1 The Error Terms Involving the Top Order Spatial Derivatives of the Acoustical Entities397
14.2 The Borderline Error Integrals404
14.3 Assumption J405
14.4 The Borderline Estimates Associated to K0408
14.4.1 Estimates for the Contribution of (14.56)408
14.4.2 Estimates for the Contribution of (14.57)417
14.5 The Borderline Estimates Associated to K1423
14.5.1 Estimates for the Contribution of(14.56)423
14.5.2 Estimates for the Contribution of(14.57)446
15 The Top Order Energy Estimates463
15.1 Estimates Associated to K1463
15.2 Estimates Associated to K0477
16 The Descent Scheme489
17 The Isoperimetric Inequality.Recovery of Assumption J.Recovery of the Bootstrap Assumption Proof of the Main Theorem503
17.1 Recovery of J—Preliminary503
17.2 The Isoperimetric Inequality505
17.3 Recovery of J—Completion509
17.4 Recovery of the Final Bootstrap Assumption510
17.5 Completion of the Proof of the Main Theorem511
18 Sufficient Conditions on the Initial Data for the Formation of a Shock in the Evolution521
19 The Structure of the Boundary of the Domain of the Maximal Solution533
19.1 Nature of Singular Hypersurface in Acoustical Differential Structure533
19.1.1 Preliminary533
19.1.2 Intrinsic View Point535
19.1.3 Invariant Curves537
19.1.4 Extrinsic View Point539
19.2 The Trichotomy Theorem for Past Null Geodesics Ending at Singular Boundary543
19.2.1 Hamiltonian Flow543
19.2.2 Asymptotic Behavior545
19.3 Transformation of Coordinates562
19.4 How H Looks Like in Rectangular Coordinates in Galilean Spacetime575
References581