From N-body problem to Euler equations

TL;DR

This paper rigorously derives the Euler hydrodynamic equations from a Hamiltonian N-particle system as N approaches infinity, without relying on stochastic dynamics or kinetic theory tools.

Contribution

It provides a direct mathematical derivation of Euler equations from Hamiltonian particle systems, avoiding standard intermediate methods.

Findings

Euler equations obtained as N tends to infinity

No use of stochastic or thermodynamic tools

Provides a rigorous mathematical framework

Abstract

This paper contains a rigorous mathematical example of direct derivation of the system of Euler hydrodynamic equations from Hamiltonian equations for N point particle system as N tends to infinity. Direct means that the following standard tools are not used in the proof: stochastic dynamics, thermodynamics, Boltzmann kinetic equations, correlation functions approach by N. N. Bogolyubov.