### 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 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 language | English (US) |
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Pages (from-to) | 523-560 |

Number of pages | 38 |

Journal | Communications In Mathematical Physics |

Volume | 155 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1993 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Olla, S., Varadhan, S. R. S., & Yau, H. T. (1993). Hydrodynamical limit for a Hamiltonian system with weak noise.

*Communications In Mathematical Physics*,*155*(3), 523-560. https://doi.org/10.1007/BF02096727