Global existence and decay for solutions of the Hele-Shaw flow with injection
We study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere decay to zero exponentially fast. On the other hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell,...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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European Mathematical Society Publishing House
2012
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| _version_ | 1797058275102949376 |
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| author | Cheng, C Coutand, D Shkoller, S |
| author_facet | Cheng, C Coutand, D Shkoller, S |
| author_sort | Cheng, C |
| collection | OXFORD |
| description | We study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere decay to zero exponentially fast. On the other hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell, the distance from the moving boundary to an expanding sphere (with time-dependent radius) also decays to zero but with an algebraic rate, which depends on the injection rate of the fluid. |
| first_indexed | 2024-03-06T19:48:09Z |
| format | Journal article |
| id | oxford-uuid:230ec71c-f428-4dcc-8b17-d57bb1c701b7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:48:09Z |
| publishDate | 2012 |
| publisher | European Mathematical Society Publishing House |
| record_format | dspace |
| spelling | oxford-uuid:230ec71c-f428-4dcc-8b17-d57bb1c701b72022-03-26T11:42:08ZGlobal existence and decay for solutions of the Hele-Shaw flow with injectionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:230ec71c-f428-4dcc-8b17-d57bb1c701b7EnglishSymplectic Elements at OxfordEuropean Mathematical Society Publishing House2012Cheng, CCoutand, DShkoller, SWe study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere decay to zero exponentially fast. On the other hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell, the distance from the moving boundary to an expanding sphere (with time-dependent radius) also decays to zero but with an algebraic rate, which depends on the injection rate of the fluid. |
| spellingShingle | Cheng, C Coutand, D Shkoller, S Global existence and decay for solutions of the Hele-Shaw flow with injection |
| title | Global existence and decay for solutions of the Hele-Shaw flow with
injection |
| title_full | Global existence and decay for solutions of the Hele-Shaw flow with
injection |
| title_fullStr | Global existence and decay for solutions of the Hele-Shaw flow with
injection |
| title_full_unstemmed | Global existence and decay for solutions of the Hele-Shaw flow with
injection |
| title_short | Global existence and decay for solutions of the Hele-Shaw flow with
injection |
| title_sort | global existence and decay for solutions of the hele shaw flow with injection |
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