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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2408.15586 |
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| _version_ | 1866914927312109568 |
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| author | Wei, Yuchong Yao, Zheng-an |
| author_facet | Wei, Yuchong Yao, Zheng-an |
| contents | In this paper, we consider a layer of viscous incompressible isotropic micropolar fluid in a uniform gravitational field of finite depth, lying above a flat rigid bottom and below the atmosphere in a three-dimensional horizontally periodic setting. The fluid dynamics are governed by gravity-driven incompressible micropolar equations. We investigate the global well-posedness for both the cases with and without surface tension. On one hand, in the case with surface tension (i.e. σ > 0), we show that the global solution decays to the equilibrium exponentially. On the other hand, in the case without surface tension (i.e. σ = 0), the solution decays to the equilibrium at an almost exponential rate. Comparing the two different cases for σ > 0 and σ = 0 reveals that the surface tension can enhance the decay rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decay Rates for Viscous Surface Waves of Isotropic Micropolar Fluids With or Without Surface Tension Wei, Yuchong Yao, Zheng-an Analysis of PDEs In this paper, we consider a layer of viscous incompressible isotropic micropolar fluid in a uniform gravitational field of finite depth, lying above a flat rigid bottom and below the atmosphere in a three-dimensional horizontally periodic setting. The fluid dynamics are governed by gravity-driven incompressible micropolar equations. We investigate the global well-posedness for both the cases with and without surface tension. On one hand, in the case with surface tension (i.e. σ > 0), we show that the global solution decays to the equilibrium exponentially. On the other hand, in the case without surface tension (i.e. σ = 0), the solution decays to the equilibrium at an almost exponential rate. Comparing the two different cases for σ > 0 and σ = 0 reveals that the surface tension can enhance the decay rate. |
| title | Decay Rates for Viscous Surface Waves of Isotropic Micropolar Fluids With or Without Surface Tension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.15586 |