Extension of Hamel paradox for the 2D exterior Navier-Stokes problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912167212613632 |
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| author | Guo, Zhengguang Hillairet, Matthieu |
| author_facet | Guo, Zhengguang Hillairet, Matthieu |
| contents | In this paper, we continue the analysis of the stationary exterior Navier-Stokes problem with interior boundary data and vanishing condition at infinity. We first show an existence result that extends a previous contribution of the second author by considering boundary data prescribing a non-trivial flux on the internal boundary. We obtain in particular that the non-uniqueness result of G. Hamel extends to an open set of internal boundary data. We then show that one way to recover uniqueness of a solution is to complement the perturbation of velocity field with a decay condition at infinity for small circulation through the interior boundary. Our method is based on a fine analysis of the linearized Navier-Stokes system around potential flows in the exterior domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extension of Hamel paradox for the 2D exterior Navier-Stokes problem Guo, Zhengguang Hillairet, Matthieu Analysis of PDEs In this paper, we continue the analysis of the stationary exterior Navier-Stokes problem with interior boundary data and vanishing condition at infinity. We first show an existence result that extends a previous contribution of the second author by considering boundary data prescribing a non-trivial flux on the internal boundary. We obtain in particular that the non-uniqueness result of G. Hamel extends to an open set of internal boundary data. We then show that one way to recover uniqueness of a solution is to complement the perturbation of velocity field with a decay condition at infinity for small circulation through the interior boundary. Our method is based on a fine analysis of the linearized Navier-Stokes system around potential flows in the exterior domain. |
| title | Extension of Hamel paradox for the 2D exterior Navier-Stokes problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.17399 |