### 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) |
---|---|

Pages (from-to) | 523-560 |

Number of pages | 38 |

Journal | Communications in Mathematical Physics |

Volume | 155 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1993 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

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

**Hydrodynamical limit for a Hamiltonian system with weak noise.** / Olla, S.; Varadhan, Srinivasa; Yau, H. T.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 155, no. 3, pp. 523-560. https://doi.org/10.1007/BF02096727

}

TY - JOUR

T1 - Hydrodynamical limit for a Hamiltonian system with weak noise

AU - Olla, S.

AU - Varadhan, Srinivasa

AU - Yau, H. T.

PY - 1993/8

Y1 - 1993/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21344483632&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344483632&partnerID=8YFLogxK

U2 - 10.1007/BF02096727

DO - 10.1007/BF02096727

M3 - Article

AN - SCOPUS:21344483632

VL - 155

SP - 523

EP - 560

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -