On putative self-similarity for incompressible 3D Euler
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911469347536896 |
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| author | Constantin, Peter Ignatova, Mihaela Vicol, Vlad |
| author_facet | Constantin, Peter Ignatova, Mihaela Vicol, Vlad |
| contents | We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similarity exponent $γ$ which governs the rate of zooming in must be larger than $2/5$. If a smooth globally self-similar blowup profile exists, and this profile satisfies an outgoing property, we prove that $γ\geq 1/2$. For axisymmetric solutions, we establish the bound $γ\geq 1/2$ in more general settings, including ones in which the outgoing property is not present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17570 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On putative self-similarity for incompressible 3D Euler Constantin, Peter Ignatova, Mihaela Vicol, Vlad Analysis of PDEs 35Q35 We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similarity exponent $γ$ which governs the rate of zooming in must be larger than $2/5$. If a smooth globally self-similar blowup profile exists, and this profile satisfies an outgoing property, we prove that $γ\geq 1/2$. For axisymmetric solutions, we establish the bound $γ\geq 1/2$ in more general settings, including ones in which the outgoing property is not present. |
| title | On putative self-similarity for incompressible 3D Euler |
| topic | Analysis of PDEs 35Q35 |
| url | https://arxiv.org/abs/2602.17570 |