Construction of low regularity strong solutions to the viscous surface wave equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914750984617984 |
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| author | Gui, Guilong Li, Yancan |
| author_facet | Gui, Guilong Li, Yancan |
| contents | We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. Here we use the Lagrangian structure of the system to homogenize the free boundary conditions, and establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no nonlinear compatibility conditions on the initial data are required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of low regularity strong solutions to the viscous surface wave equations Gui, Guilong Li, Yancan Analysis of PDEs 35Q30, 35R35, 76D03 We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. Here we use the Lagrangian structure of the system to homogenize the free boundary conditions, and establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no nonlinear compatibility conditions on the initial data are required. |
| title | Construction of low regularity strong solutions to the viscous surface wave equations |
| topic | Analysis of PDEs 35Q30, 35R35, 76D03 |
| url | https://arxiv.org/abs/2404.08448 |