Self-similar algebraic spiral vortex sheets of 2-D incompressible Euler equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912362219438080 |
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| author | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| author_facet | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| contents | This paper provides the first rigorous construction of the self-similar algebraic spiral vortex sheet solutions to the 2-D incompressible Euler equations. These solutions are believed to represent the typical roll-up pattern of vortex sheets after the formation of curvature singularities. The most challenging part of this paper is to handle the Cauchy integral for the algebraic spiral curve, which falls outside the classical theory of singular integral operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-similar algebraic spiral vortex sheets of 2-D incompressible Euler equations Shao, Feng Wei, Dongyi Zhang, Zhifei Analysis of PDEs This paper provides the first rigorous construction of the self-similar algebraic spiral vortex sheet solutions to the 2-D incompressible Euler equations. These solutions are believed to represent the typical roll-up pattern of vortex sheets after the formation of curvature singularities. The most challenging part of this paper is to handle the Cauchy integral for the algebraic spiral curve, which falls outside the classical theory of singular integral operators. |
| title | Self-similar algebraic spiral vortex sheets of 2-D incompressible Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.03309 |