Stability of Navier-Stokes equations with a free surface
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911856688365568 |
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| author | Cheng, Xing Zheng, Yunrui |
| author_facet | Cheng, Xing Zheng, Yunrui |
| contents | We consider the viscous incompressible fluids in a three-dimensional horizontally periodic domain bounded below by a fixed smooth boundary and above by a free moving surface. The fluid dynamics are governed by the Navier-Stokes equations with the effect of gravity and surface tension on the free surface. We develop a global well-posedness theory by a nonlinear energy method in low regular Sobolev spaces with several techniques, including: the horizontal energy-dissipation estimates, a new tripled bootstrap argument inspired by Guo and Tice [Arch. Ration. Mech. Anal.(2018)]. Moreover, the solution decays asymptotically to the equilibrium in an exponential rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Navier-Stokes equations with a free surface Cheng, Xing Zheng, Yunrui Analysis of PDEs We consider the viscous incompressible fluids in a three-dimensional horizontally periodic domain bounded below by a fixed smooth boundary and above by a free moving surface. The fluid dynamics are governed by the Navier-Stokes equations with the effect of gravity and surface tension on the free surface. We develop a global well-posedness theory by a nonlinear energy method in low regular Sobolev spaces with several techniques, including: the horizontal energy-dissipation estimates, a new tripled bootstrap argument inspired by Guo and Tice [Arch. Ration. Mech. Anal.(2018)]. Moreover, the solution decays asymptotically to the equilibrium in an exponential rate. |
| title | Stability of Navier-Stokes equations with a free surface |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.16585 |