Matteo Colangeli 
From Kinetic Models to Hydrodynamics 
Some Novel Results

​​From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts.​ The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.​

Table of Content

​​​ 1. Introduction.- 2. From the Phase Space to the Boltzmann Equation.- 3. Methods of Reduced Description.- 4. Hydrodynamic Spectrum of Simple Fluids.- 5. Hydrodynamic Fluctuations from the Boltzmann Equation.- 6. 13 Moment Grad System.- 7. Conclusions.- References. ​ ​​