Communications in Mathematical Physics

, Volume 155, Issue 3, pp 523–560 | Cite as

Hydrodynamical limit for a Hamiltonian system with weak noise

  • S. Olla
  • S. R. S. Varadhan
  • H. T. Yau
Article

Abstract

Starting from a general hamiltonian system with superstable pairwise potential, we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles. We prolve that, in the scaling limit, the time conserved quantities, energy, momenta and density, satisfy the Euler equation of conservation laws up to a fixed timet provided that the Euler equation has a smooth solution with a given initial data up to timet. The strength of the noise term is chosen to be very small (but nonvanishing) so that it disappears in the scaling limit.

Keywords

Neural Network Statistical Physic Complex System Initial Data Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • S. Olla
    • 1
  • S. R. S. Varadhan
    • 1
  • H. T. Yau
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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