Well-posedness of the two-dimensional stationary Navier--Stokes equations around a uniform flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913419341332480 |
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| author | Fujii, Mikihiro Tsurumi, Hiroyuki |
| author_facet | Fujii, Mikihiro Tsurumi, Hiroyuki |
| contents | In this paper, we consider the solvability of the two-dimensional stationary Navier--Stokes equations on the whole plane $\mathbb{R}^2$. In [6], it was proved that the stationary Navier--Stokes equations on $\mathbb{R}^2$ is ill-posed for solutions around zero. In contrast, considering solutions around the non-zero constant flow, the perturbed system has a better regularity in the linear part, which enables us to prove the unique existence of solutions in the scaling critical spaces of the Besov type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the two-dimensional stationary Navier--Stokes equations around a uniform flow Fujii, Mikihiro Tsurumi, Hiroyuki Analysis of PDEs In this paper, we consider the solvability of the two-dimensional stationary Navier--Stokes equations on the whole plane $\mathbb{R}^2$. In [6], it was proved that the stationary Navier--Stokes equations on $\mathbb{R}^2$ is ill-posed for solutions around zero. In contrast, considering solutions around the non-zero constant flow, the perturbed system has a better regularity in the linear part, which enables us to prove the unique existence of solutions in the scaling critical spaces of the Besov type. |
| title | Well-posedness of the two-dimensional stationary Navier--Stokes equations around a uniform flow |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.05012 |