Matteo Colangeli From Kinetic Models to Hydrodynamics

Annotation

From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtainhydrodynamic equations from afundamental description usingkinetic theory models and the Boltzmann equation. The work isa surveyof anactive research area,which aims tobridgetime and length scalesfrom 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 thenonequilibrium 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 hydrodynamiclimit. The invariant manifold method paves the way to establish aneeded bridgebetween Boltzmann equation theory and a particle-based theory ofhydrodynamics. Finally, the authorexploresthe 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.