The incompressible Navier-Stokes for the nonlinear discrete velocity models

Details The incompressible Navier-Stokes for the nonlinear discrete velocity models The incompressible Navier-Stokes for the nonlinear discrete velocity models

2003-06-18

arxiv.org/abs/nlin/0306036v1

J. Nonlinear Math. Phys., volume 9, no. 4 (2002) 426-445

Nonlinear Sciences

Exactly Solvable and Integrable Systems

arxiv version is already official

Scientific paper

We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian. Appropriately scaled families solutions of discrete Boltzmann equation are shown to have fluctuations that locally in time converge strongly to a limit governed by a solution of Incompressible Navier--Stokes provided that the initial fluctuation is smooth, and converges to appropriate initial data. As applications of our results, we study the Carleman model and the one-dimensional Broadwell model.

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