Abstract
We study a stochastic particle system on the lattice whose particles move freely according to a simple exclusion process and change velocities during collisions preserving energy and momentum. In the hydrodynamic limit, under diffusive space-time scaling, the local velocity field u satisfies the incompressible Navier–Stokes equation, while the temperature field θ solves the heat equation with drift u. The results are also extended to include a suitably resealed external force.
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Benois, O., Esposito, R. & Marra, R. Navier–Stokes Limit for a Thermal Stochastic Lattice Gas. Journal of Statistical Physics 96, 653–713 (1999). https://doi.org/10.1023/A:1004618924291
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DOI: https://doi.org/10.1023/A:1004618924291