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Conclusions

  • Matteo ColangeliEmail author
Chapter
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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this work, we employed the invariant manifold method to derive closed hydrodynamic equations from some kinetic models. The main novelty of our approach stems from the use of a nonperturbative technique that allows us to sum exactly the classical Chapman–Enskog expansion. The method postulates a separation between slow and fast moments, and allows us to extract the slow invariant manifold in the space of distribution functions.

Keywords

Entropy Production Local Equilibrium Invariant Manifold Knudsen Number Local Thermodynamic Equilibrium 
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References

  1. 1.
    A. N. Gorban, I. V. Karlin, P. Ilg, and H. C. Öttinger, Corrections and Enhancements of Quasi-equilibrium States, J. Non-Newtonian Fluid Mech. 96, 203 (2001).zbMATHCrossRefGoogle Scholar
  2. 2.
    A. N. Gorban, I. V. Karlin, H. C. Öttinger, and L. L. Tatarinova, Ehrenfest’s Argument Extended to a Formalism of Nonequilibrium Thermodynamics, Phys. Rev. E 63, 066124 (2001).CrossRefGoogle Scholar
  3. 3.
    A. N. Gorban and I. V. Karlin, Macroscopic Dynamics through Coarse-Graining: A Solvable Example, Phys. Rev. E 65, 026116 (2002).Google Scholar
  4. 4.
    H. C. Öttinger, Betond Equilibrium Thermodynamics (Wiley, 2005).Google Scholar
  5. 5.
    B. J. Alder and W. E. Alley, Generalized Hydrodynamics, Phys. Today 37, 56 (1984).CrossRefGoogle Scholar
  6. 6.
    A. N. Gorban and I. V. Karlin, Thermodynamic Parameterization, Physica A 190, 393 (1992).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. N. Gorban, I. V. Karlin, and A. Yu. Zinovyev, Constructive Methods of Invariant Manifolds for Kinetic Problems, Phys. Reports 396, 197 (2004).MathSciNetCrossRefGoogle Scholar

Copyright information

© Matteo Colangeli 2013

Authors and Affiliations

  1. 1.Department of MathematicsPolitecnico di TorinoTorinoItaly

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