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.
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Communicated by J. L. Lebowitz
Research partially supported by U.S. National Science Foundation grants DMS 89001682, DMS 920-1222 and a grant from ARO, DAAL03-92-G-0317
Research partially supported by U.S. National Science Foundation grants DMS-9101196, DMS-9100383, and PHY-9019433-A01, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship
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Olla, S., Varadhan, S.R.S. & Yau, H.T. Hydrodynamical limit for a Hamiltonian system with weak noise. Commun.Math. Phys. 155, 523–560 (1993). https://doi.org/10.1007/BF02096727
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DOI: https://doi.org/10.1007/BF02096727