On pressureless Euler equation with external force
Mathematical Physics
2024-05-27 v2 math.MP
Exactly Solvable and Integrable Systems
Fluid Dynamics
Abstract
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence of gradient catastrophes. It is shown that in even dimensions the constructed solutions are periodic in time for particular subclasses of external forces. Several particular examples in one, two and three dimensions are considered, including the case of Coriolis external force.
Cite
@article{arxiv.2405.10646,
title = {On pressureless Euler equation with external force},
author = {B. G. Konopelchenko and G. Ortenzi},
journal= {arXiv preprint arXiv:2405.10646},
year = {2024}
}
Comments
reference added 24 pages, 4 figures