Hydrodynamical limit for a Hamiltonian system with weak noise

S. Olla, S. R.S. Varadhan, H. T. Yau

Research output: Contribution to journalArticlepeer-review


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 time t provided that the Euler equation has a smooth solution with a given initial data up to time t. The strength of the noise term is chosen to be very small (but nonvanishing) so that it disappears in the scaling limit.

Original languageEnglish (US)
Pages (from-to)523-560
Number of pages38
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Aug 1993

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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