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Journal of Statistical Physics

, Volume 74, Issue 5–6, pp 981–1004 | Cite as

On the derivation of the incompressible Mavier-Stokes equation for Hamiltonian particle systems

  • R. Esposito
  • R. Marra
Articles

Abstract

We consider a Hamiltonian paticle system interacting by means of a pair potetial. We look at the behavior of the system on a space scale of order ε-1, times of order ε-2 and mean velocities of order ε, with ε a scale parameter. Assuming that the phase space density of the particles is give by a series in ε (the analog of the Chapman-Enskog expansion), the behavior of the system under this rescaling is described, to the lowest order in ε, by the incompressible Navier-Stokes equations. The viscosity is given in terms of microscopic correlations, and its expression agrees with the Green-Kubo formula.

Key Words

Hydrodynamic limit incompressible Navier-Stokes equations particle systems 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • R. Esposito
    • 1
  • R. Marra
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomeItaly
  2. 2.Dipartimento di FisicaUniversità di Roma tor VergataRomeItaly

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