Free boundary problems for the two-dimensional Euler equations in exterior domains
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913402513784832 |
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| author | Cao, Daomin Fan, Boquan Zhan, Weicheng |
| author_facet | Cao, Daomin Fan, Boquan Zhan, Weicheng |
| contents | In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points adheres to slip boundary conditions and maintains a constant norm on the boundary, along with certain additional conditions at infinity, then the domain is the complement of a disk, and the flow is circular, namely the streamlines are concentric circles. Additionally, we establish that in the entire plane, if all the stagnation points of a steady Euler flow coincidentally form a disk, then, under certain additional reasonable conditions near the stagnation points and at infinity, the flow must be circular. The proof is based on a refinement of the method of moving planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free boundary problems for the two-dimensional Euler equations in exterior domains Cao, Daomin Fan, Boquan Zhan, Weicheng Analysis of PDEs In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points adheres to slip boundary conditions and maintains a constant norm on the boundary, along with certain additional conditions at infinity, then the domain is the complement of a disk, and the flow is circular, namely the streamlines are concentric circles. Additionally, we establish that in the entire plane, if all the stagnation points of a steady Euler flow coincidentally form a disk, then, under certain additional reasonable conditions near the stagnation points and at infinity, the flow must be circular. The proof is based on a refinement of the method of moving planes. |
| title | Free boundary problems for the two-dimensional Euler equations in exterior domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.16134 |