Abstract
We introduce a class of stochastic models of particles on the cubic lattice ℤd with velocities and study the hydrodynamical limit on the diffusive spacetime scale. Assuming special initial conditions corresponding to the incompressible regime, we prove that in dimensiond≧3 there is a law of large numbers for the empirical density and the rescaled empirical velocity field. Moreover the limit fields satisfy the corresponding incompressible Navier-Stokes equations, with viscosity matrices characterized by a variational formula, formally equivalent to the Green-Kubo formula.
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Communicated by J.L. Lebowitz
Partially supported by GNFM-CNR and MURST.
Partially supported by GNFM-CNR, INFN and MURST.
Partially supported by U.S. National Science Foundation grant 9403462 and David and Lucile Packard Foundation Fellowship.
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Esposito, R., Marra, R. & Yau, H.T. Navier-Stokes equations for stochastic particle systems on the lattice. Commun.Math. Phys. 182, 395–455 (1996). https://doi.org/10.1007/BF02517896
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DOI: https://doi.org/10.1007/BF02517896