Hydrodynamical limit for a Hamiltonian system with weak noise

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)523-560
Number of pages38
JournalCommunications in Mathematical Physics
Volume155
Issue number3
DOIs
StatePublished - Aug 1993

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Hamiltonian Systems
Scaling Limit
Euler Equations
Momentum
scaling
Conserved Quantity
Stochastic Dynamics
Smooth Solution
Term
conservation laws
Conservation Laws
Pairwise
kinetic energy
momentum
Energy

ASJC Scopus subject areas

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

Cite this

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

In: Communications in Mathematical Physics, Vol. 155, No. 3, 08.1993, p. 523-560.

Research output: Contribution to journalArticle

Olla, S. ; Varadhan, Srinivasa ; Yau, H. T. / Hydrodynamical limit for a Hamiltonian system with weak noise. In: Communications in Mathematical Physics. 1993 ; Vol. 155, No. 3. pp. 523-560.
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