​​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.​

​​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.​