Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas: Treated as a Branch of Rational Mechanics

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Page iii

Copyright page
Page iv

Dedication
Page v

Prologue
Pages xv-xx

Acknowledgments
Pages xxi-xxii
C. Truesdell

Notation
Pages xxiii-xxiv

List of Special Symbols
Pages xxv-xxvii

Chapter I Continuum Theories of Fluids
Pages 3-18

Chapter II The Stokes-Kirchhoff Gas, Some of Its Peculiarities, and Some of Its Flows
Pages 19-36

Chapter III The Molecular Density, the Definitions of Gross Fields, and the Equation of Evolution
Pages 39-50

Chapter IV Some Limits of Agreement between Kinetic Theories and Classical Fluid Mechanics
Pages 51-60

Chapter V The Differential Operators of the Kinetic Theory
Pages 61-68

Chapter VI The Dynamics of Molecular Encounters
Pages 69-89

Chapter VII The Maxwell Collisions Operator. Kinetic Constitutive Relations. The Total Collisions Operator and Bilinear Form
Pages 91-103

Chapter VIII Boltzmann's Monotonicity Theorem. The Maxwellian Density. Analogues of the Caloric and its Flux
Pages 105-127

Chapter IX The Maxwell-Boltzmann Equation. Maxwell's Consistency Theorem and Equation of Transfer
Pages 131-136

Chapter X Kinetic Equilibrium and Gross Equilibrium. Locally Maxwellian Solutions
Pages 137-143

Chapter XI Boltzmann's H-Theorem
Pages 145-172

Chapter XII The Collisions Operator for Some Special Kinetic Constitutive Relations, Especially Maxwellian Molecules
Pages 175-186

Chapter XIII The Pressures and the Energy Flux in a Gas of Maxwellian Molecules. Maxwell's Relaxation Theorem and Evaluation of Viscosity and Thermal Conductivity
Pages 187-196

Chapter XIV Homo-energetic Simple Shearing of a Gas of Maxwellian Molecules
Pages 197-218

Chapter XV General Solution for the Pressures in Homo-energetic Affine Flows of a Gas of Maxwellian Molecules
Pages 219-234

Chapter XVI The General System of Equations for the Moments in a Gas of Maxwellian Molecules. Ikenberry's Theorem on the Structure of Collisions Integrals
Pages 237-259

Chapter XVII Grad's Formal Evaluation of Collisions Integrals, and his Method of Approximating the Initial-value Problem
Pages 261-291

Chapter XVIII Existence Theory for the General Initial-value Problem. Part I: Molecules with Intermolecular Forces of Infinite Range
Pages 295-303

Chapter XIX Convergence Theorems and the Domain of the Collisions Operator
Pages 305-317

Chapter XX Existence Theory for the General Initial-value Problem. Part II: Place-dependent Solutions for Molecules with a Cut-off
Pages 319-333

Chapter XXI Existence Theory for the General Initial-value Problem. Part III: Spatially Homogeneous Solutions for Molecules with a Cut-off
Pages 335-371

Chapter XXII Hilbert's Formal Iterative Procedure for Calculating Gas-dynamic Solutions. The Assertion of Gross Causality. The Hilbert Mapping
Pages 375-396

Chapter XXIII Grossly Determined Solutions. The Equations of Gross Determinism
Pages 397-427

Chapter XXIV The Method of Stretched Fields for Approximating Gross Determiners. Use of it to Obtain the Results of Enskog's Procedure
Pages 429-505

Chapter XXV The Maxwellian Iteration of Ikenberry & Truesdell
Pages 507-540

Chapter XXVI Convergence and Divergence of Atemporal Maxwellian Iteration in Flows for Which an Exact Solution is Known. Failure of the Higher Iterates to Improve the Asymptotic Approximation
Pages 541-558

Epilogue
Pages 559-567

List of Works Cited Review Article
Pages 569-577

Index of Authors Cited
Pages 579-581

Index of Matters Treated
Pages 582-593