Abstract
This paper contains a rigorous mathematical example of direct derivation of the system of Euler hydrodynamic equations from the Hamiltonian equations for an N point particle system as N → ∞. “Direct” means that the following standard tools are not used in the proof: stochastic dynamics, thermodynamics, Boltzmann kinetic equations, and the correlation functions approach due to Bogolyubov.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics (1845, Kiev, Acad of Science of USSR, 1945).
C. Morrey, “On the Derivation of the Equations of Hydrodynamics from Statistical Mechanics,” Comm. Pure Appl. Math. 8, 279–326 (1955).
M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids (Springer, 1993).
R. Esposito, J. Lebowitz, and R. Marra, “On the Derivation of Hydrodynamics from the Boltzmann Equation,” Phys. Fluids 11 (8), 2354–2366 (1999).
R. Esposito and R. Marra, Incompressible Fluids on Three Levels: Hydrodynamic, Kinetic, Microscopic. Mathematical Analysis of Phenomena in Fluid and Plasma Dynamics (RIMS, Kyoto, 1993).
C. Boldrighini, R. L. Dobrushin and Yu. M. Sukhov, “One-Dimensional Hard Rod Caricature of Hydrodynamics,” J. Statist. Phys. 31 (3), (1983).
A. Chorin and J. Marsden, A Mathematical Introduction to Fluid Mechanics (Third Ed. Springer, 2000).
C. Siegel and J. Moser, Lectures on Celestial Mechanics (Springer-Verlag, 1971).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lykov, A.A., Malyshev, V.A. From the N-body problem to Euler equations. Russ. J. Math. Phys. 24, 79–95 (2017). https://doi.org/10.1134/S106192081701006X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106192081701006X