From Kinetic Models to Hydrodynamics

From Kinetic Models to Hydrodynamicsserves as an introduction to theasymptotic methods necessaryto obtain hydrodynamic equations from afundamental description usingkinetic theory models and the Boltzmann equation. The work isa survey of anactive research area,which aims tobridgetime and length scales from the particle-like description inherent inBoltzmann equationtheory to afully established "continuum" approachtypical of macroscopiclaws of physics.Theauthorsheds light on a new method-usinginvariant manifolds-which addresses a functional equation for the nonequilibrium single-particle distribution function. This methodallows one to find exact and thermodynamically consistent expressions for:hydrodynamic modes;transport coefficient expressions for hydrodynamic modes;andtransport coefficients of a fluidbeyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish aneeded bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the authorexploresthe 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.