稀薄气体的数学理论

《稀薄气体的数学理论》是2009年高等教育出版社出版的图书，作者是切尔奇纳尼。本书讲述了稀薄气体的数学理论(Boltzmann方程的数学理论)中的三个主要问题。

• 中文名 稀薄气体的数学理论
• 定价 28.40
• 出版社 高等教育出版社
• 作者 切尔奇纳尼
• 出版时间 2009年02月

内容简介

　　直到1 994年的理论发展，包括BoItzm来自ann方程是怎样从经典力学推出来的，即BoItzmann方程是怎样从Liouville方程推出来的;Boltzmann方程解的存在性和唯一性问题;Boltzmann方程与流体力学的关系，即EuIer方程和Navier-Stokes方程是怎样从Liouv况爱也压水极ille方程推出来的。

图书目录

　　Introduction

　　1 Historical Introduction

　　1.1 What is a Gas? From the Billiard Table to Boyles Law

　　1.2 Brief History of Kinetic Theory

　　2 I360百科nformal De束协rivation of the Boltzmann Equation

　　2.1 The Phase Space and the Liouville Equati乐呼鱼屋督球参on

　　2.2 Bol航提tzmanns Argument in a Modern Perspective

　　2.3 Molecu次片故脱或以么呢刘lar Chaos. Critique and Justificatio湖蛋素解帮这n

　　2.4 The BBGKY Hierarchy

　　2.5 The Boltzmann Hierar日手余从治chy and Its Re将子步lation to the Boltzmann Equat限子湖移量工八ion

　　3 Elementary Properties of the S么到胜模值物olutions

　　3.1 C青ollision Invariants 33

　　3.2 The Boltzmann Inequality and the Ma底新议群控后xwell Distr丝防ibutions

　　3.3 The Macroscopic Balance Equations

　　3.4 The H-Theorem

　　3.5 Losc引行先病优看外同hmidts Parado即丰尽此洲坏干况晶x

　　3.6 Poincares 学坚然密滑具岩兴Recurrence and Zermelos Paradox

　　3.7 Equi关钟黑librium Sta海板村命扩块免然tes and Maxwellian Distributions

　　3.8 Hydrodynamical Limit and Other Scalings

　　4 Rigorous Validity of the Boltzmann Equation

　　4.1 Significance of the Problem

　　4.2 Hard-Sphere Dynamics

　　4.3 Transition to L1. The Liouville Equation and the BBGKY Hierarchy Revisited

　　4.4 Rigorous Validity of the Boltzmann Equation

　　4.5 Validity of the Boltzmann Equation for a Rare Cloud of Gas in the Vacuum

　　4.6 Interpretation

　　4.7 The Emergence of Irreversibility

　　4.8 More on the Boltzmann Hierarchy

　　Appendix 4.A More about Hard-Sphere Dynamics

　　Appendix 4.B A Rigorous Derivation of the BBGKY Hierarchy

　　Appendix 4.C Uchiyamas Example

　　5 Existence and Uniqueness Results

　　5.1 Preliminary Remarks

　　5.2 Existence from Validity, and Overview

　　5.3 A General Global Existence Result

　　5.4 Generalizations and Other Remarks

　　Appendix 5.A

　　6 The Initial Value Problem for the Homogeneous Boltzmann Equation

　　6.1 An Existence Theorem for a Modified Equation

　　6.2 Removing the Cutoff: The L1-Theory for the Full Equation

　　6.3 The L∞-Theory and Classical Solutions

　　6.4 Long Time Behavior

　　6.5 Further Developments and Comments

　　Appendix 6.A

　　Appendix 6.B

　　Appendix 6.C

　　7 Perturbations of Equilibria and Space Homogeneous Solutions

　　7.1 The Linearized Collision Operator

　　7.2 The Basic Properties of the Linearized Collision Operator

　　7.3 Spectral Properties of the Fourier-Transformed, Linearized Boltzmann Equation

　　7.4 The Asymptotic Behavior of the Solution of the Cauchy Problem for the Linearized Boltzmann Equation

　　7.5 The Global Existence Theorem for the Nonlinear Equation

　　7.6 Extensions: The Periodic Case and Problems in One and Two Dimensions

　　7.7 A Further Extension: Solutions Close to a Space Homogeneous Solution

　　8 Boundary Conditions

　　8.1 Introduction

　　8.2 The Scattering Kernel

　　8.3 The Accommodation Coefficients

　　8.4 Mathematical Models

　　8.5 A Remarkable Inequality

　　9 Existence Results for Initial-Boundary and Boundary Value Problems

　　9.1 Preliminary Remarks

　　9.2 Results on the Traces

　　9.3 Properties of the Free-Streaming Operator

　　9.4 Existence in a Vessel with Isothermal Boundary

　　9.5 Rigorous Proof of the Approach to Equilibrium

　　9.6 Perturbations of Equilibria

　　9.7 A Steady Problem

　　9.8 Stability of the Steady Flow Past an Obstacle

　　9.9 Concluding Remarks

　　10 Particle Simulation of the Boltzmann Equation

　　10.1 Rationale amd Overview

　　10.2 Low Discrepancy Methods

　　10.3 Birds Scheme

　　11 Hydrodynamical Limits

　　11.1 A Formal Discussion

　　11.2 The Hilbert Expansion

　　11.3 The Entropy Approach to the Hydrodynamical Limit

　　11.4 The Hydrodynamical Limit for Short Times

　　11.5 Other Scalings and the Incompressible Navier-Stokes Equations

　　12 Open Problems and New Directions

　　Author Index

　　Subject Index