From Kinetic Models to Hydrodynamics

From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtainhydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a surveyof an active research area, which aims to bridge time and length scalesfrom 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 thenonequilibrium 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 hydrodynamiclimit. The invariant manifold method paves the way to establish a needed bridgebetween Boltzmann equation theory and a particle-based theory ofhydrodynamics. Finally, the author explores the ambitious and longstanding taskof obtaining hydrodynamic constitutive equations from their kinetic counterparts. 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.