Sticky particle dynamics with interactions
Analysis of PDEs
2014-09-16 v1 Mathematical Physics
math.MP
Abstract
We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a differential inclusion on the space of transport maps, in particular when a sticky particle dynamics is assumed. We study a discrete particle approximation and we prove global existence and stability results for solutions of this system. In the particular case of the Euler-Poisson system in the attractive regime our approach yields an explicit representation formula for the solutions.
Cite
@article{arxiv.1201.2350,
title = {Sticky particle dynamics with interactions},
author = {Yann Brenier and Wilfrid Gangbo and Giuseppe Savaré and Michael Westdickenberg},
journal= {arXiv preprint arXiv:1201.2350},
year = {2014}
}