The mathematical theory of dilute gases = 稀薄气体的数学理论 /

　　Introduction
　　
　　1 Historical Introduction
　　 1.1 What is a Gas? From the Billiard Table to Boyle's Law
　　 1.2 Brief History of Kinetic Theory
　　2 Informal Derivation of the Boltzmann Equation
　　 2.1 The Phase Space and the Liouville Equation
　　 2.2 Boltzmann's Argument in a Modern Perspective
　　 2.3 Molecular Chaos. Critique and Justification
　　 2.4 The BBGKY Hierarchy
　　 2.5 The Boltzmann Hierarchy and Its Relation to the Boltzmann Equation
　　3 Elementary Properties of the Solutions
　　 3.1 Collision Invariants 33
　　 3.2 The Boltzmann Inequality and the Maxwell Distributions
　　 3.3 The Macroscopic Balance Equations
　　 3.4 The H-Theorem
　　 3.5 Loschmidt's Paradox
　　 3.6 Poincare's Recurrence and Zermelo's Paradox
　　 3.7 Equilibrium States 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 Uchiyama's 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 Bird's 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