From Kinetic Models to Hydrodynamics

Some Novel Results

  • Matteo Colangeli

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Matteo Colangeli
    Pages 1-2
  3. Matteo Colangeli
    Pages 23-35
  4. Matteo Colangeli
    Pages 37-47
  5. Matteo Colangeli
    Pages 75-94
  6. Matteo Colangeli
    Pages 95-96

About this book


​​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.​


Boltzmann equation theory Grad’s moment method system Navier-Stokes Fourier approximation hydrodynamic equations, modes, fluctuations kinetic theory models the invariant manifold method

Authors and affiliations

  • Matteo Colangeli
    • 1
  1. 1., Department of MathematicsPolitecnico di TorinoTorinoItaly

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