 96216 J. Quastel and H.T. Yau
 Lattice gases, large deviations, and the incompressible
NavierStokes equations
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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 NavierStokes
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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