From Kinetic Models to Hydrodynamics

​​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.​