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Some mathematical problems in the dynamics of stochastic second-grade fluids
Thesis (PhD)--University of Pretoria, 2011.
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University of Pretoria
2013
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| _version_ | 1867613443839754240 |
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| access_status_str | Open Access |
| author2 | Sango, Mamadou |
| author_browse | Sango, Mamadou |
| author_facet | Sango, Mamadou |
| collection | Thesis |
| dc_rights_str_mv | © 2010 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, 2011. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/25715 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:36:14.350Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| 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:2263/25715 Some mathematical problems in the dynamics of stochastic second-grade fluids Sango, Mamadou paulrazafi@gmail.com Razafimandimby, Paul Andre Stochastic system Bidimensional second grade fluid Lipschitz conditions UCTD Thesis (PhD)--University of Pretoria, 2011. In the present work we initiate the investigation of a stochastic system of evolution partial differential equations modelling the turbulent flows of a bidimensional second grade fluid. Global existence and uniqueness of strong probabilistic solution (but weak in the sense of partial differential equations) are expounded. We also give two results on the long time behavior of the strong probabilistic solution of this stochastic model. Mainly we prove that the strong probabilistic solution of our stochastic model converges exponentially in mean square to the stationary solution of the time-independent second grade fluids equations if the deterministic part of the external force does not depend on time. In the time-dependent case the strong probabilistic solution decays exponentially in mean square. These results are obtained under Lipschitz conditions on the forces entering in the model considered. We also establish the global existence of weak probabilistic solution when the Lipschitz condition on the forces no longer holds. Finally, we show that under suitable conditions on the data we can construct a sequence of strong probabilistic solutions of the stochastic second grade fluid that converges to the strong probabilistic solution of the stochastic Navier-Stokes equations when the stress modulus á tends to zero. All these results are new for the stochastic second-grade fluid and generalize the corresponding results obtained for the deterministic second-grade fluids. Mathematics and Applied Mathematics unrestricted 2013-09-06T23:38:54Z 2011-06-27 2013-09-06T23:38:54Z 2011-04-05 2011-06-27 2011-06-21 Thesis Razafimandimby, PA 2010, Some mathematical problems in the dynamics of stochastic second-grade fluids, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/25715 > D11/377/ag http://hdl.handle.net/2263/25715 http://upetd.up.ac.za/thesis/available/etd-06212011-120758/ © 2010 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 application/pdf application/pdf application/pdf University of Pretoria |
| spellingShingle | Stochastic system Bidimensional second grade fluid Lipschitz conditions UCTD Some mathematical problems in the dynamics of stochastic second-grade fluids |
| title | Some mathematical problems in the dynamics of stochastic second-grade fluids |
| title_full | Some mathematical problems in the dynamics of stochastic second-grade fluids |
| title_fullStr | Some mathematical problems in the dynamics of stochastic second-grade fluids |
| title_full_unstemmed | Some mathematical problems in the dynamics of stochastic second-grade fluids |
| title_short | Some mathematical problems in the dynamics of stochastic second-grade fluids |
| title_sort | some mathematical problems in the dynamics of stochastic second grade fluids |
| topic | Stochastic system Bidimensional second grade fluid Lipschitz conditions UCTD |
| url | http://hdl.handle.net/2263/25715 http://upetd.up.ac.za/thesis/available/etd-06212011-120758/ |