On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917414430572544 |
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| author | Miller, Evan Tsai, Tai-Peng |
| author_facet | Miller, Evan Tsai, Tai-Peng |
| contents | In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension $d\geq 4$, axisymmetric, swirl-free solutions of the Euler equation have properties which could allow finite-time singularity formation of a form that is excluded when $d=3$, and we prove a conditional blowup result for axisymmetric, swirl-free solutions of the Euler equation in dimension $d\geq 4$. The condition which must be imposed on the solution in order to imply blowup becomes weaker as $d\to +\infty$, suggesting the dynamics are becoming much more singular as the dimension increases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13406 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions Miller, Evan Tsai, Tai-Peng Analysis of PDEs 35Q31, 76B47, 76B03 In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension $d\geq 4$, axisymmetric, swirl-free solutions of the Euler equation have properties which could allow finite-time singularity formation of a form that is excluded when $d=3$, and we prove a conditional blowup result for axisymmetric, swirl-free solutions of the Euler equation in dimension $d\geq 4$. The condition which must be imposed on the solution in order to imply blowup becomes weaker as $d\to +\infty$, suggesting the dynamics are becoming much more singular as the dimension increases. |
| title | On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions |
| topic | Analysis of PDEs 35Q31, 76B47, 76B03 |
| url | https://arxiv.org/abs/2204.13406 |