On a 3D Stokes eigenvalue problem under Navier slip-with-friction boundary conditions and applications to Navier-Stokes equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910874663387136 |
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| author | Berselli, Luigi C. Falocchi, Alessio Sannipoli, Rossano |
| author_facet | Berselli, Luigi C. Falocchi, Alessio Sannipoli, Rossano |
| contents | In this paper we consider, by means of a precise spectral analysis, the 3D Navier-Stokes equations endowed with Navier slip-with-friction boundary conditions. We study the problem in a very simple geometric situation as the region between two parallel planes, with periodicity along the two planes. This setting, which is often used in the theory of boundary layers, requires some special treatment for what concerns the functional setting and allows us to characterize in a rather explicit manner eigenvalues and eigenfunctions of the associated Stokes problem. These, will be then used in order to identify infinite dimensional classes of data leading to global strong solutions for the corresponding evolution Navier-Stokes equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_07496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a 3D Stokes eigenvalue problem under Navier slip-with-friction boundary conditions and applications to Navier-Stokes equations Berselli, Luigi C. Falocchi, Alessio Sannipoli, Rossano Analysis of PDEs Spectral Theory Primary 35Q30, Secondary 47A75 In this paper we consider, by means of a precise spectral analysis, the 3D Navier-Stokes equations endowed with Navier slip-with-friction boundary conditions. We study the problem in a very simple geometric situation as the region between two parallel planes, with periodicity along the two planes. This setting, which is often used in the theory of boundary layers, requires some special treatment for what concerns the functional setting and allows us to characterize in a rather explicit manner eigenvalues and eigenfunctions of the associated Stokes problem. These, will be then used in order to identify infinite dimensional classes of data leading to global strong solutions for the corresponding evolution Navier-Stokes equations. |
| title | On a 3D Stokes eigenvalue problem under Navier slip-with-friction boundary conditions and applications to Navier-Stokes equations |
| topic | Analysis of PDEs Spectral Theory Primary 35Q30, Secondary 47A75 |
| url | https://arxiv.org/abs/2407.07496 |