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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.

Keywords

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

R2 v1 2026-06-28T16:30:35.889Z