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Mixed variational problems associated with stationary viscous incompressible free boundary flows
Bibliography: pages 93-97.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613284404822016 |
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| access_status_str | Open Access |
| author | Le Roux, Christiaan |
| author2 | Reddy, B Daya |
| author_browse | Le Roux, Christiaan Reddy, B Daya |
| author_facet | Reddy, B Daya Le Roux, Christiaan |
| author_sort | Le Roux, Christiaan |
| collection | Thesis |
| description | Bibliography: pages 93-97. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15965 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:41.762Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15965 Mixed variational problems associated with stationary viscous incompressible free boundary flows Le Roux, Christiaan Reddy, B Daya Mathematics and Applied Mathematics Bibliography: pages 93-97. A strategy that is often used in the study of capillary free boundary (FB) problems for viscous incompressible flows is the following: (1) Ignore one of the boundary conditions at the FB and prove that for every chosen position of the FB the resultant problem, here called the auxiliary problem (AP), is well posed. (2) Establish regularity results for the solution of the AP. (3) Using (2) and the remaining boundary condition, determine the position of the FB. We study the existence and uniqueness of the weak solution(s) to the AP, i.e., step (1), under minimal regularity constraints on the data and domain. The analysis is carried out for stationary two-dimensional flows, governed by either the Stokes or Navier-Stokes equations, in the context of four standard examples. A Green's formula is derived which allows the AP to be formulated as a mixed variational problem in which the pressure and normal stress appear as Lagrange multipliers. Existence and uniqueness results are obtained by using the Ladyzhenskaya-Babuska-Brezzi theory for mixed problems. By analogy with step (3), the dependence of the normal stress on the position of the FB is investigated. 2015-12-28T06:03:37Z 2015-12-28T06:03:37Z 1991 Master Thesis Masters MSc http://hdl.handle.net/11427/15965 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Le Roux, Christiaan Mixed variational problems associated with stationary viscous incompressible free boundary flows |
| thesis_degree_str | Master's |
| title | Mixed variational problems associated with stationary viscous incompressible free boundary flows |
| title_full | Mixed variational problems associated with stationary viscous incompressible free boundary flows |
| title_fullStr | Mixed variational problems associated with stationary viscous incompressible free boundary flows |
| title_full_unstemmed | Mixed variational problems associated with stationary viscous incompressible free boundary flows |
| title_short | Mixed variational problems associated with stationary viscous incompressible free boundary flows |
| title_sort | mixed variational problems associated with stationary viscous incompressible free boundary flows |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/15965 |
| work_keys_str_mv | AT lerouxchristiaan mixedvariationalproblemsassociatedwithstationaryviscousincompressiblefreeboundaryflows |