Overview
\u200b\u200bFrom Kinetic Models to Hydrodynamics\xa0serves as an introduction to the\xa0asymptotic methods necessary\xa0to obtainhydrodynamic equations from a\xa0fundamental description using\xa0kinetic theory models and the Boltzmann equation. \xa0The work is\xa0a surveyof an\xa0active research area,\xa0which aims to\xa0bridge\xa0time and length scalesfrom the particle-like description inherent in\xa0Boltzmann equation\xa0theory to a\xa0fully established "continuum" approach\xa0typical of macroscopic\xa0laws of physics.The\xa0author\xa0sheds light on a new method-using\xa0invariant manifolds-which addresses a functional equation for thenonequilibrium single-particle distribution function. \xa0This method\xa0allows one to find exact and thermodynamically consistent expressions for:\xa0hydrodynamic modes;\xa0transport coefficient expressions for hydrodynamic modes;\xa0and\xa0transport coefficients of a fluid\xa0beyond the traditional hydrodynamiclimit. \xa0The invariant manifold method paves the way to establish a\xa0needed bridgebetween Boltzmann equation theory and a particle-based theory ofhydrodynamics. \xa0Finally, the author\xa0explores\xa0the ambitious and longstanding taskof obtaining hydrodynamic constitutive equations from their kinetic counterparts.\u200b The work isintended for specialists in kinetic theory-or more generally statisticalmechanics-and will provide a bridge between a physical and mathematicalapproach to solve real-world problems.\u200b
