可压缩流与欧拉方程
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作者(美)克里斯托多罗,缪爽 著
出版社高等教育出版社
ISBN9787040400984
出版时间2014-08
版次1
装帧精装
开本16开
纸张胶版纸
页数580页
字数99999千字
定价128元
上书时间2024-05-27
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基本信息
书名:可压缩流与欧拉方程
定价：128元
作者:(美)克里斯托多罗,缪爽 著
出版社：高等教育出版社
出版日期：2014-08-01
ISBN：9787040400984
字数：700000
页码：580
版次：1
装帧：精装
开本：16开
商品重量：
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内容提要
本书主要考虑三维空间中，其初值在单位球面外为常值的任意状态方程的经典可压缩欧拉方程。当初值与常状态差别适当小时，我们建立的定理可以给出关于解的完整描述。特别地，解的定义域的边界包含一个奇异部分，在那里波前的密度将会趋向于无穷大，从而激波形成。在本书中，我们采用几何化方法，得到了关于这个奇异部分的完整的几何描述以及解在这部分性态的详细分析，其核心概念是声学时空流形。
目录
1 Compressible Flow and Non-linear Wave Equations 1.1 Euler's Equations 1.2 Irrotational Flow and the Nonlinear Wave Equatio 1.3 The Equation of Variations and the Acoustical Metric 1.4 The Fundamental Variations2 The Basic Geometric Constructio 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 H3 The Acoustical Structure Equations 3.1 The Acoustical Structure Equations 3.2 The Derivatives of the Rectangular Components of L and T4 The Acoustical Curvature 4.1 Expressions for Curvature Tensor 4.2 Regularity for the Acoustical Structure Equations as μ → 0 4.3 A Remark5 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 Proof6 Construction of Commutation Vectorfields 6.1 Commutation Vectorfields and Their Deformation Tensors 6.2 Preliminary Estimates for the Deformation Tensors7 Outline of the Derived Estimates of Each Order 7.1 The Inhomogeneous Wave Equations for the Higher Order Variations. The Recursion Formula for the Source Functions 7.2 The First Term in ρ 7.3 The Estimates of the Contribution of the First Term in ρn to the Error Integrals8 Regularization of the Propagation Equation for □trX. Estimates for the Top Order Angular Derivatives of X 8.1 Preliminary 8.1.1 Regularization of The Propagation Equatio 8.1.2 Propagation Equations for Higher Order Angular Derivatives 8.1.3 Elliptic Theory on St,u 8.1.4 Preliminary Estimates for the Solutions of the Propagation Equations 8.2 Crucial Lemmas Concerning the Behavior of μ 8.3 The Actual Estimates for the Solutions of the Propagation Equations9 Regularization of the Propagation Equation for □μ. Estimates for the Top Order Spatial Derivatives of μ 9.1 Regularization of the Propagation Equatio 9.2 Propagation Equations for the Higher Order Spatial Derivatives 9.3 Elliptic Theory on St,u 9.4 The Estimates for the Solutions of the Propagation Equations10 Control 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 Pl11 Control 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,l12 Recovery of the Acoustical Assumptions Estimates for Up to the Next to the Top Order Angular Derivatives of X and Spatial Derivatives of μ 12.1 Estimates for λi, y', yi and r. Establishing the Hypothesis H0 12.2 The Coercivity Hypothesis H1, H2 and H2'. Estimates for X' 12.3 Estimates for Higher Order Derivatives of X' and μ13 Derivation of the Basic Properties of μ14 The 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)15 The Top Order Energy Estimates 15.1 Estimates Associated to K1 15.2 Estimates Associated to K016 The Descent Scheme17 The Isoperimetric Inequality. Recovery of Assumption J. Recovery of the Bootstrap Assumption. Proof of the Mai Theorem 17.1 Recovery of J--Preliminary 17.2 The Isoperimetric Inequality 17.3 Recovery of J--Completio 17.4 Recovery of the Final Bootstrap Assumptio 17.5 Completion of the Proof of the Main Theorem18 Sufficient Conditions on the Initial Data for the Formation of a Shock in the Evolutio19 The Structure of the Boundary of the Domain of the Maximal Solutio 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 SpacetimeReferences
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