Time-zero limits of Kaden's spirals and 2D Euler

Fuente: arXiv
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Auteurs principaux: Bieganowski, Bartosz, Cieślak, Tomasz, Siemianowski, Jakub
Format: Preprint
Publié: 2023
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author Bieganowski, Bartosz
Cieślak, Tomasz
Siemianowski, Jakub
author_facet Bieganowski, Bartosz
Cieślak, Tomasz
Siemianowski, Jakub
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_15356
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Time-zero limits of Kaden's spirals and 2D Euler
Bieganowski, Bartosz
Cieślak, Tomasz
Siemianowski, Jakub
Analysis of PDEs
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.
title Time-zero limits of Kaden's spirals and 2D Euler
topic Analysis of PDEs
url https://arxiv.org/abs/2305.15356