From kinetic models to hydrodynamics : some novel results

Cover......Page 1
From Kinetic Models to Hydrodynamics......Page 3
Preface......Page 6
Acknowledgments......Page 8
Contents......Page 9
7 Conclusions......Page 11
References......Page 12
2.1 The Phase Space Description......Page 13
2.2 The Boltzmann Equation......Page 19
2.2.1 H-Theorem and the Maxwellian Distribution......Page 25
2.3 Hydrodynamic Limit and Other Scalings......Page 26
2.4 Linearized Collision Integrals and Kinetic Models......Page 28
References......Page 30
3.1 The Bogoliubov Hypothesis and Macroscopic Equations......Page 32
3.2 The Hilbert and the Chapman--Enskog Methods......Page 37
3.3 Grad's Moment Method......Page 39
3.4 The Invariant Manifold Theory......Page 40
References......Page 44
4.1 Correlations in Space and Time......Page 46
4.2 Linearized Hydrodynamics and Collective Modes......Page 50
References......Page 55
5.1 Eigenfrequencies of the Boltzmann Equation......Page 57
5.2 The Invariant Manifold Technique......Page 60
5.3 Coordinate Representation and Symmetries......Page 63
5.4 The BGK Kinetic Model......Page 67
5.5 The Maxwell Molecules Gas......Page 70
5.5.1 Hydrodynamic Modes and Transport Coefficients......Page 73
5.5.2 Short-Wavelength Hydrodynamics......Page 76
References......Page 79
6.1 Derivation of the 13-Moment System from the Boltzmann Equation......Page 82
6.2 Hydrodynamics from the Linearized One-Dimensional Grad's System......Page 83
6.2.1 Invariance Equations......Page 87
6.2.2 Exact Hydrodynamic Solutions......Page 88
6.2.3 Hyperbolic Transformation for Exact Hydrodynamics......Page 91
6.3 Exact Hydrodynamics from Three-Dimensional Linearized Grad's Equations......Page 94
References......Page 100
References......Page 102