A lattice gas model for the incompressible navier-stokes equation

J. Beltran; C. Landim

doi:10.1214/07-AIHP125

A lattice gas model for the incompressible navier-stokes equation

J. Beltran
, C. Landim

IMCA
LMRS - Laboratoire de Mathématiques Raphaël Salem

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	886-914
Number of pages	29
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	44
Issue number	5
DOIs	https://doi.org/10.1214/07-AIHP125
State	Published - Oct 2008
Externally published	Yes

Keywords

Hydrodynamic limit
Incompressible navier-stokes equation
Interacting particle systems

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10.1214/07-AIHP125

Cite this

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abstract = "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.",

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AU - Landim, C.

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N2 - 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.

AB - 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.

KW - Hydrodynamic limit

KW - Incompressible navier-stokes equation

KW - Interacting particle systems

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 5

ER -

A lattice gas model for the incompressible navier-stokes equation

Abstract

Keywords

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