Macroscopic Non-uniqueness and Limits of Hamiltonian Dynamics

TL;DR

This paper constructs explicit examples demonstrating non-uniqueness and spontaneous energy generation in the compressible Euler system by analyzing limits of Hamiltonian molecular dynamics as the number of molecules grows.

Contribution

It introduces explicit constructions of non-uniqueness and energy anomalies in fluid models derived from Hamiltonian particle systems, highlighting limits of classical dynamics.

Findings

Examples of non-uniqueness in Euler equations

Instances of spontaneous energy generation

Limits of molecular dynamics lead to non-unique solutions

Abstract

We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The examples come from rescalings of well-posed, deterministic systems of molecules that either collide elastically or interact via singular pair potentials.