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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.09856 |
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| _version_ | 1866914834317049856 |
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| author | Han, Jingwen Wang, Yun Xie, Chunjing |
| author_facet | Han, Jingwen Wang, Yun Xie, Chunjing |
| contents | In this paper, we investigate the Liouville-type theorems for axisymmetric solutions to steady Navier-Stokes system in a layer domain. The both cases for the flows supplemented with no-slip boundary and Navier boundary conditions are studied. If the width of the outlet grows at a rate less than $R^{\frac{1}{2}}$, any bounded solution is proved to be trivial. Meanwhile, if the width of the outlet grows at a rate less than $R^{\frac{4}{5}}$, every D-solution is proved to be trivial. The key idea of the proof is to establish a Saint-Venant type estimate that characterizes the growth of Dirichlet integral of nontrivial solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville-type theorems for Axisymmetric solutions to steady Navier-Stokes system in a layer domain Han, Jingwen Wang, Yun Xie, Chunjing Analysis of PDEs In this paper, we investigate the Liouville-type theorems for axisymmetric solutions to steady Navier-Stokes system in a layer domain. The both cases for the flows supplemented with no-slip boundary and Navier boundary conditions are studied. If the width of the outlet grows at a rate less than $R^{\frac{1}{2}}$, any bounded solution is proved to be trivial. Meanwhile, if the width of the outlet grows at a rate less than $R^{\frac{4}{5}}$, every D-solution is proved to be trivial. The key idea of the proof is to establish a Saint-Venant type estimate that characterizes the growth of Dirichlet integral of nontrivial solutions. |
| title | Liouville-type theorems for Axisymmetric solutions to steady Navier-Stokes system in a layer domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.09856 |