Well-posedness for the classical Stefan problem and the zero surface tension limit
We develop a framework for a {\em unified} treatment of well-posedness for the Stefan problem with and without surface tension. In the absence of surface tension, we provide new estimates for the regularity of the moving free-surface. We construct solutions as a limit of a carefully chosen sequence...
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| Format: | Journal article |
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2011
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| _version_ | 1797060629882732544 |
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| author | Hadzic, M Shkoller, S |
| author_facet | Hadzic, M Shkoller, S |
| author_sort | Hadzic, M |
| collection | OXFORD |
| description | We develop a framework for a {\em unified} treatment of well-posedness for the Stefan problem with and without surface tension. In the absence of surface tension, we provide new estimates for the regularity of the moving free-surface. We construct solutions as a limit of a carefully chosen sequence of approximate solutions to our so-called $\kappa $-problem, in which moving surface is regularized and the boundary condition is modified. We conclude by proving that solutions of the Stefan problem with positive surface tension $\sigma$ converge to solutions of the classical Stefan problem as $\sigma\to0$. |
| first_indexed | 2024-03-06T20:19:48Z |
| format | Journal article |
| id | oxford-uuid:2d6736f3-fae2-4269-af45-52f6d3234304 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:19:48Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:2d6736f3-fae2-4269-af45-52f6d32343042022-03-26T12:42:43ZWell-posedness for the classical Stefan problem and the zero surface tension limitJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2d6736f3-fae2-4269-af45-52f6d3234304Symplectic Elements at Oxford2011Hadzic, MShkoller, SWe develop a framework for a {\em unified} treatment of well-posedness for the Stefan problem with and without surface tension. In the absence of surface tension, we provide new estimates for the regularity of the moving free-surface. We construct solutions as a limit of a carefully chosen sequence of approximate solutions to our so-called $\kappa $-problem, in which moving surface is regularized and the boundary condition is modified. We conclude by proving that solutions of the Stefan problem with positive surface tension $\sigma$ converge to solutions of the classical Stefan problem as $\sigma\to0$. |
| spellingShingle | Hadzic, M Shkoller, S Well-posedness for the classical Stefan problem and the zero surface tension limit |
| title | Well-posedness for the classical Stefan problem and the zero surface
tension limit |
| title_full | Well-posedness for the classical Stefan problem and the zero surface
tension limit |
| title_fullStr | Well-posedness for the classical Stefan problem and the zero surface
tension limit |
| title_full_unstemmed | Well-posedness for the classical Stefan problem and the zero surface
tension limit |
| title_short | Well-posedness for the classical Stefan problem and the zero surface
tension limit |
| title_sort | well posedness for the classical stefan problem and the zero surface tension limit |
| work_keys_str_mv | AT hadzicm wellposednessfortheclassicalstefanproblemandthezerosurfacetensionlimit AT shkollers wellposednessfortheclassicalstefanproblemandthezerosurfacetensionlimit |