Abstract
We derive rigorously the fluid-dynamical equations for the one-dimensional discrete velocity model, considered in [1], directly from the BBGKY hierarchy of this model. The model we consider is not a mathematical one like the well-known Broadwell models of the Boltzmann equation [2]. It is also different from the Broadwell model of the BBGKY hierarchy considered in [3], the stochastic model dealt with in [4] and lattice gas cellular automata as well ( see e.g.[5] and references therein). It is a deterministic model which can be regarded as physically realistic. The scheme that we present is apparently the first where the fluid limit for such a system is obtained in a rigorous way from the BBGKY hierarchy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V.I. Gerasimenko, V.V. Gorunovich,The Bogoliubov’s equations for a one-dimensional particle system, Dokl. Ak. Nauk. Ukr. ,8, 34 (1991).
K. Uchiyama, On the Boltzmann-Grad limit for the Broadwell model of Boltzmann equation, Jour. Stat. Phys. ,52, 331 (1988).
R. Caflisch, G.Papanicolaou, The fluid-dynamical limit of of non-linear model Boltzmann equa tion, Com. Pur. Appl. Math. ,32, 589 (1979).
S.Caprino, A.DeMasi, E.Presutti, M.Pulvirenti, A derivation of the Broadwell equation, Comm. Math .Phys. ,135, 433 (1991).
M.H. Ernst, “Statistical mechanics of cellular automata fluids,” Course 2, J.P. Hansen, D. Levesque and J. Zinn-Justin, eds., Elsevier Science Publishers B.V. (1991).
J. Boldrighini, R. Dobrushin, Yu. Suhov, One-dimensional hard rod caricature of hydrodynam ics, Journ. Stat. Phys. 31, 577 (1983).
J. Lebowitz, J. Percus, J .Sykes, Time evolution of the total distribution function of a 1- dimensional system of hard rods, Phys. Rev. ,721, 224 (1968).
N.N. Bogoliubov, The hydrodynamics equations in statistical mechanics, in: “Sbo-rnik trudov”, vol. 2, Nauk. dumka, Kiev (1970).
Z. Salsburg, R. Zwanzig, and J. Kirkwood, Molecular distribution functions in a one-dimensional fluid, Journ. Chem. Phys. ,21, 1098 (1953).
C. Morrey, On the derivation of the equations of hydrodynamics from statistical mechanics, Comm. Pure. Appl. Math. ,8, 279 (1955).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gorunovich, V. (1994). The Fluid-Dynamical Limit for the BBGKY Hierarchy of a Discrete Velocity Model. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_37
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2460-1_37
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6047-6
Online ISBN: 978-1-4615-2460-1
eBook Packages: Springer Book Archive