Local Rigidity of the Couette Flow for the Stationary Triple-Deck Equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929347001057280 |
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| author | Iyer, Sameer Maekawa, Yasunori |
| author_facet | Iyer, Sameer Maekawa, Yasunori |
| contents | The Triple-Deck equations are a classical boundary layer model which describes the asymptotics of a viscous flow near the separation point, and the Couette flow is an exact stationary solution to the Triple-Deck equations. In this paper we prove the local rigidity of the Couette flow in the sense that there are no other stationary solutions near the Couette flow in a scale invariant space. This provides a stark contrast to the well-studied stationary Prandtl counterpart, and in particular offers a first result towards the rigidity question raised by R. E. Meyer in 1983. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_10532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Rigidity of the Couette Flow for the Stationary Triple-Deck Equations Iyer, Sameer Maekawa, Yasunori Analysis of PDEs The Triple-Deck equations are a classical boundary layer model which describes the asymptotics of a viscous flow near the separation point, and the Couette flow is an exact stationary solution to the Triple-Deck equations. In this paper we prove the local rigidity of the Couette flow in the sense that there are no other stationary solutions near the Couette flow in a scale invariant space. This provides a stark contrast to the well-studied stationary Prandtl counterpart, and in particular offers a first result towards the rigidity question raised by R. E. Meyer in 1983. |
| title | Local Rigidity of the Couette Flow for the Stationary Triple-Deck Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.10532 |