Microscopic solutions of the Boltzmann-Enskog equation in the series representation
Mathematical Physics
2018-02-19 v1 Analysis of PDEs
Dynamical Systems
math.MP
Abstract
The Boltzmann-Enskog equation for a hard sphere gas is known to have so called microscopic solutions, i.e., solutions of the form of time-evolving empirical measures of a finite number of hard spheres. However, the precise mathematical meaning of these solutions should be discussed, since the formal substitution of empirical measures into the equation is not well-defined. Here we give a rigorous mathematical meaning to the microscopic solutions to the Boltzmann-Enskog equation by means of a suitable series representation.
Keywords
Cite
@article{arxiv.1802.05926,
title = {Microscopic solutions of the Boltzmann-Enskog equation in the series representation},
author = {Mario Pulvirenti and Sergio Simonella and Anton Trushechkin},
journal= {arXiv preprint arXiv:1802.05926},
year = {2018}
}