Abstract
We prove the existence of uncountably-many physical scattering maps for non-spherical hard particles which, when used to construct global-in-time weak solutions of Newton’s equations of motion, conserve the total linear momentum, angular momentum and kinetic energy of the particle system for all time. We prove this result by first exhibiting the non-uniqueness of a classical solution to a constrained Monge–Ampère equation posed on Euclidean space, and then applying the deep existence theory of Ballard for hard particle dynamics. In the final section of the article, we briefly discuss the relevance of our observations to the statistical mechanics of hard particle systems.
Original language | English |
---|---|
Pages (from-to) | 2055–2083 |
Number of pages | 29 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 235 |
Early online date | 18 Nov 2019 |
DOIs | |
Publication status | Published - Mar 2020 |
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering