Time-zero limits of Kaden's spirals and 2D Euler
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909565609574400 |
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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 |