| Summary: | 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 methodusing�invariant manifoldswhich 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 theoryor more generally statistical mechanicsand will provide a bridge between a physical and mathematical approach to solve real-world problems.
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