Large time decay of the Oseen flow in exterior domains subject to the Navier slip-with-friction boundary condition
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917263989276672 |
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| author | Hishida, Toshiaki |
| author_facet | Hishida, Toshiaki |
| contents | Consider the motion of a viscous incompressible fluid filling a 3D exterior domain $Ω$ subject to the Navier slip-with-friction boundary condition as well as outflow at infinity. For the Oseen system as the linearization, we discuss the resolvent set under a certain relationship among the geometry of the boundary $\partialΩ$, friction coefficient $α(x)$ and the outflow $u_\infty$. We then study the regularity of the resolvent near the origin in the complex plane to develop $L^q$-$L^r$ decay estimates of the Oseen semigroup provided that $α(x)+u_\infty\cdotν(x)/2\geq 0$ for every $x\in\partialΩ$, where $ν(x)$ stands for the outward unit normal to the boundary $\partialΩ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large time decay of the Oseen flow in exterior domains subject to the Navier slip-with-friction boundary condition Hishida, Toshiaki Analysis of PDEs 35B40, 76D07 Consider the motion of a viscous incompressible fluid filling a 3D exterior domain $Ω$ subject to the Navier slip-with-friction boundary condition as well as outflow at infinity. For the Oseen system as the linearization, we discuss the resolvent set under a certain relationship among the geometry of the boundary $\partialΩ$, friction coefficient $α(x)$ and the outflow $u_\infty$. We then study the regularity of the resolvent near the origin in the complex plane to develop $L^q$-$L^r$ decay estimates of the Oseen semigroup provided that $α(x)+u_\infty\cdotν(x)/2\geq 0$ for every $x\in\partialΩ$, where $ν(x)$ stands for the outward unit normal to the boundary $\partialΩ$. |
| title | Large time decay of the Oseen flow in exterior domains subject to the Navier slip-with-friction boundary condition |
| topic | Analysis of PDEs 35B40, 76D07 |
| url | https://arxiv.org/abs/2602.09804 |