CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE
Free surface flow in a Hele-Shaw cell is considered. It has been known for some time that when the fluid region is contracting, a finite time blow-up can occur, in which a cusp forms in the free surface, the solution does not exist beyond the time of blow-up. Examples are presented of this blow-up,...
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| Format: | Journal article |
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1986
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| _version_ | 1826264626746097664 |
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| author | Howison, S |
| author_facet | Howison, S |
| author_sort | Howison, S |
| collection | OXFORD |
| description | Free surface flow in a Hele-Shaw cell is considered. It has been known for some time that when the fluid region is contracting, a finite time blow-up can occur, in which a cusp forms in the free surface, the solution does not exist beyond the time of blow-up. Examples are presented of this blow-up, and also of a new process in which a cusp of a different type forms in the free surface, but after which the solution continues to exist. After a transformation of the dependent variable (the pressure) the new cusps are related to permissible singularities in the free boundary of the 'obstacle' problem. |
| first_indexed | 2024-03-06T20:10:51Z |
| format | Journal article |
| id | oxford-uuid:2a83d7cd-66cf-4ef8-8703-e9fe08d92449 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:10:51Z |
| publishDate | 1986 |
| record_format | dspace |
| spelling | oxford-uuid:2a83d7cd-66cf-4ef8-8703-e9fe08d924492022-03-26T12:25:27ZCUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACEJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a83d7cd-66cf-4ef8-8703-e9fe08d92449Symplectic Elements at Oxford1986Howison, SFree surface flow in a Hele-Shaw cell is considered. It has been known for some time that when the fluid region is contracting, a finite time blow-up can occur, in which a cusp forms in the free surface, the solution does not exist beyond the time of blow-up. Examples are presented of this blow-up, and also of a new process in which a cusp of a different type forms in the free surface, but after which the solution continues to exist. After a transformation of the dependent variable (the pressure) the new cusps are related to permissible singularities in the free boundary of the 'obstacle' problem. |
| spellingShingle | Howison, S CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE |
| title | CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE |
| title_full | CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE |
| title_fullStr | CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE |
| title_full_unstemmed | CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE |
| title_short | CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE |
| title_sort | cusp development in hele shaw flow with a free surface |
| work_keys_str_mv | AT howisons cuspdevelopmentinheleshawflowwithafreesurface |