Time-zero limits of Kaden's spirals and 2D Euler
Analysis of PDEs
2025-04-08 v2
Abstract
The present note is devoted to the studies of the relation of the time-zero limits of Kaden's spirals and the 2D Euler equation. It is shown that the time-zero limits of Kaden's spirals satisfy inhomogeneous 2D Euler in a weak sense. As a corollary, the necessity of both, the decay of spherical averages around the origin of the spiral as well as the velocity matching condition, for the 2D Euler equation to hold in a weak sense, is shown. Finally, some preliminary results concerning the Kaden spirals are obtained.
Cite
@article{arxiv.2305.15356,
title = {Time-zero limits of Kaden's spirals and 2D Euler},
author = {Bartosz Bieganowski and Tomasz Cieślak and Jakub Siemianowski},
journal= {arXiv preprint arXiv:2305.15356},
year = {2025}
}
Comments
to appear in Lecture Notes in Nonlinear Analysis