Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions
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| Format: | Preprint |
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2024
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| _version_ | 1866916716211077120 |
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| author | Schwab, Russell Tu, Son Turanova, Olga |
| author_facet | Schwab, Russell Tu, Son Turanova, Olga |
| contents | In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravity). We prove global well-posedness for the corresponding Hamilton-Jacobi-Bellmann equation with bounded, uniformly continuous initial data, in all dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions Schwab, Russell Tu, Son Turanova, Olga Analysis of PDEs 35B51, 35R09, 35R35, 45K05, 47G20, 49L25, 76D27, 35Q35, 76B03, 35D35, 35D40 In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravity). We prove global well-posedness for the corresponding Hamilton-Jacobi-Bellmann equation with bounded, uniformly continuous initial data, in all dimensions. |
| title | Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions |
| topic | Analysis of PDEs 35B51, 35R09, 35R35, 45K05, 47G20, 49L25, 76D27, 35Q35, 76B03, 35D35, 35D40 |
| url | https://arxiv.org/abs/2404.10972 |