no. 5
A lattice gas model for the incompressible Navier-Stokes equation
Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 5, pp. 886-914.

Nous retrouvons l'équation de Navier-Stokes comme limite incompressible d'un gas sur réseau où les particules peuvent sauter sur des distances mésoscopiques. Le résultat est valable en toute dimension supposant l'existence d'une solution lisse de l'équation de Navier-Stokes en un intervale de temps donné. La démonstration ne dépend pas des méthodes non-gradients ou l'analyse multi-échelle grâce aux sauts de longue portée.

We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier-Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.

DOI : 10.1214/07-AIHP125
Classification : 60K35, 82C22
Mots clés : interacting particle systems, hydrodynamic limit, incompressible Navier-Stokes equation 
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Beltrán, J.; Landim, C. A lattice gas model for the incompressible Navier-Stokes equation. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 5, pp. 886-914. doi : 10.1214/07-AIHP125. http://www.numdam.org/articles/10.1214/07-AIHP125/

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