On the Initial Boundary-Value Problem in the Kinetic Theory of Hard Particles I: Non-existence
Classical Analysis and ODEs
2018-05-15 v1 Classical Physics
Abstract
In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of associated boundary conditions, we identify initial conditions for which there do not exist local-in-time weak solutions of Newton's equations of motion. To our knowledge, this is the first time the necessity of rolling in the energy-conserving dynamics of strictly-convex rigid bodies has been demonstrated. This study was, in part, motivated by a recent observation of Palffy-Muhoray, Virga, Wilkinson and Zheng on the interpenetration of strictly-convex rigid bodies.
Keywords
Cite
@article{arxiv.1805.04611,
title = {On the Initial Boundary-Value Problem in the Kinetic Theory of Hard Particles I: Non-existence},
author = {Mark Wilkinson},
journal= {arXiv preprint arXiv:1805.04611},
year = {2018}
}