Global Well-posedness of Compressible Viscous Surface Waves without Surface Tension
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912097265254400 |
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| author | Sun, Ting Wang, Yanjin |
| author_facet | Sun, Ting Wang, Yanjin |
| contents | We consider the free boundary problem for a layer of compressible viscous barotropic fluid lying above a fixed rigid bottom and below the atmosphere of positive constant pressure. The fluid dynamics is governed by the compressible Navier--Stokes equations with gravity, and the effect of surface tension is neglected on the upper free boundary. We prove the global well-posedness of the reformulated problem in flattening coordinates near the equilibrium in both two and three dimensions without any low frequency assumption of the initial data. The key ingredients here are the new control of the {\it Eulerian spatial derivatives} of the solution, which benefits a crucial nonlinear cancellation of the highest order spatial regularity of the free boundary, and the time weighted energy estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Well-posedness of Compressible Viscous Surface Waves without Surface Tension Sun, Ting Wang, Yanjin Analysis of PDEs 35B40, 35Q30, 35R35, 76N06, 76N10 We consider the free boundary problem for a layer of compressible viscous barotropic fluid lying above a fixed rigid bottom and below the atmosphere of positive constant pressure. The fluid dynamics is governed by the compressible Navier--Stokes equations with gravity, and the effect of surface tension is neglected on the upper free boundary. We prove the global well-posedness of the reformulated problem in flattening coordinates near the equilibrium in both two and three dimensions without any low frequency assumption of the initial data. The key ingredients here are the new control of the {\it Eulerian spatial derivatives} of the solution, which benefits a crucial nonlinear cancellation of the highest order spatial regularity of the free boundary, and the time weighted energy estimates. |
| title | Global Well-posedness of Compressible Viscous Surface Waves without Surface Tension |
| topic | Analysis of PDEs 35B40, 35Q30, 35R35, 76N06, 76N10 |
| url | https://arxiv.org/abs/2410.23653 |