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Second grade fluids with boundery conditions
Thesis (PhD)--University of Pretoria, 1997.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613505691058176 |
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| access_status_str | Open Access |
| author2 | Sauer, N. (Niko) |
| author_browse | Sauer, N. (Niko) |
| author_facet | Sauer, N. (Niko) |
| collection | Thesis |
| dc_rights_str_mv | © 2021 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD)--University of Pretoria, 1997. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/83255 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:13.330Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/83255 Second grade fluids with boundery conditions Sauer, N. (Niko) Le Roux, Christiaan UCTD Second grade fluids boundery conditions Thesis (PhD)--University of Pretoria, 1997. It is well-known that non-Newtonian fluids such as polymers melts do not satisfy the usual adherence boundary condition. On the other hand, the available theory relies heavily on the no-slip assumption. The purpose of this work is to establish the well-posedness of the initial-boundary-value problem for flows of second grade fluids subject to general partial slip boundary conditions. It is assumed that the fluid satisfies the usual thermodynamical restrictions, that the domain of flow is bounded and simply connected, and that the slip yield stress is zero. The proof is based on a fixed-point formulation of the problem which decomposes it into three linear ones: a Stokes type problem and two transport problems. After proving the solvability of these auxiliary problems by the Faedo-Galerkin method, the existence of a unique classical solution, local in time, is established by means of a Schauder fixed point theorem. Then global a priori estimates are derived to obtain a unique global classical solution for sufficiently small data and large viscosity. The solution is found to be stable under mild restrictions on the slip operator. Mathematics and Applied Mathematics PhD Unrestricted 2022-01-12T06:00:53Z 2022-01-12T06:00:53Z 19/8/2021 1997 Thesis * http://hdl.handle.net/2263/83255 en © 2021 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Second grade fluids boundery conditions Second grade fluids with boundery conditions |
| title | Second grade fluids with boundery conditions |
| title_full | Second grade fluids with boundery conditions |
| title_fullStr | Second grade fluids with boundery conditions |
| title_full_unstemmed | Second grade fluids with boundery conditions |
| title_short | Second grade fluids with boundery conditions |
| title_sort | second grade fluids with boundery conditions |
| topic | UCTD Second grade fluids boundery conditions |
| url | http://hdl.handle.net/2263/83255 |