Self-similar algebraic spiral solution of 2-D incompressible Euler equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908338379292672 |
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| author | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| author_facet | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| contents | In this paper, we prove the existence of self-similar algebraic spiral solutions for 2-D incompressible Euler equations for the initial vorticity of the form $|y|^{-\frac1μ}\ \mathringω(θ)$ with $μ>\frac12$ and $\mathringω\in L^1(\mathbb T)$ satisfying $m$-fold symmetry ($m\geq 2$) and a dominant condition. As an important application, we prove the existence of weak solution when $\mathringω$ is a Radon measure on $\mathbb T$ with $m$-fold symmetry, which is related to the vortex sheet solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05182 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-similar algebraic spiral solution of 2-D incompressible Euler equations Shao, Feng Wei, Dongyi Zhang, Zhifei Analysis of PDEs In this paper, we prove the existence of self-similar algebraic spiral solutions for 2-D incompressible Euler equations for the initial vorticity of the form $|y|^{-\frac1μ}\ \mathringω(θ)$ with $μ>\frac12$ and $\mathringω\in L^1(\mathbb T)$ satisfying $m$-fold symmetry ($m\geq 2$) and a dominant condition. As an important application, we prove the existence of weak solution when $\mathringω$ is a Radon measure on $\mathbb T$ with $m$-fold symmetry, which is related to the vortex sheet solution. |
| title | Self-similar algebraic spiral solution of 2-D incompressible Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.05182 |