96-216 J. Quastel and H.-T. Yau

Lattice gases, large deviations, and the incompressible Navier-Stokes equations (469K, ps) May 21, 96

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Abstract. We study the incompressible limit for a class of stochastic particle systems on the cubic lattice $\ZZ^d,~d=3$. For initial distributions corresponding to arbitrary macroscopic $L^2$ initial data the distributions of the evolving empirical momentum densities are shown to have a weak limit supported entirely on global weak solutions of the incompressible Navier-Stokes equations. Furthermore explicit exponential rates for the convergence (large deviations) are obtained. The probability to violate the divergence free condition decays at rate at least $\exp\{-\e^{-d+1}\}$ while the probability to violate the momentum conservation equation decays at rate $\exp\{-\e^{-d+2}\}$ with an explicit rate function given by an $H_{-1}$ norm.

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