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Uniqueness of pressureless flow
Abstract
We consider the pressureless Euler equations in one spatial dimension. These equations model the dynamics of particles on a line that interact only through perfectly inelastic collisions. The flow was first shown to be unique for given initial conditions by Huang and Wang, assuming the entropy and the strong initial continuity of energy conditions hold. In this paper, we prove an analogous uniqueness theorem using a Lagrangian interpretation. The key ingredients are showing that each solution satisfying the entropy condition and an initial kinetic energy bound has this particular type of Lagrangian interpretation and a monotonicity inequality involving conditional expectation.
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BibTeX
@misc{hynd2026uniqueness,
title = {{Uniqueness of pressureless flow}},
author = {Ryan Hynd and Hwa Kil Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11927},
eprint = {2610.11927},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11927},
}
RIS
TY - UNPB
TI - Uniqueness of pressureless flow
AU - Ryan Hynd
AU - Hwa Kil Kim
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11927
UR - https://arxiv.org/abs/2610.11927
AB - We consider the pressureless Euler equations in one spatial dimension. These equations model the dynamics of particles on a line that interact only through perfectly inelastic collisions. The flow was first shown to be unique for given initial conditions by Huang and Wang, assuming the entropy and the strong initial continuity of energy conditions hold. In this paper, we prove an analogous uniqueness theorem using a Lagrangian interpretation. The key ingredients are showing that each solution satisfying the entropy condition and an initial kinetic energy bound has this particular type of Lagrangian interpretation and a monotonicity inequality involving conditional expectation.
ER -