One-Dimensional Hard-Rod Caricature of Hydrodynamics: Navier-Stokes Correction

Boldrighini, C. and Dobrushin, R. L. and Suhov, Yu. M. (1990) One-Dimensional Hard-Rod Caricature of Hydrodynamics: Navier-Stokes Correction. (Preprint)

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Abstract

One-dimensional system of hard-rod particles of length a is studied in the hydrodynamical limit. The Navier-Stokes correction to Euler's equation is found for an initial locally-equilibrium family of states of constant density ρ ϵ [0,a^(-1)). The correction is given, at t~0, by the non-linear second-order differential operator (Bf)(q,v) = (a^2/2)(∂/∂q)[∫dw|v-w|f(q,w)(∂/∂q)f(q,v) - f(q,v)∫dw|v-w|(∂/∂q)f(q,w)](1-ρa)^(-1) where f(q,v) is the (hydrodynamical) density at a point q ϵ R^1 of the species of particles with velocity v ϵ R^1.

Item Type:	Article
Uncontrolled Keywords:	hard-rod time-dynamics, hydrodynamical limit, Euler’s equation, locally-equilibrium family of states, Navier-Stokes correction
Divisions:	School of Theoretical Physics > Preprints
Date Deposited:	19 Jun 2018 14:15
Last Modified:	16 Dec 2022 00:33
URI:	https://dair.dias.ie/id/eprint/772

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