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Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations
Thesis (PhD)--University of Pretoria, 2010.
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University of Pretoria
2013
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| _version_ | 1867613652138328064 |
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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, 2010. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/25566 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:39:32.610Z |
| 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:2263/25566 Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations Sango, Mamadou gadeugoue@yahoo.fr Deugoue, Gabriel Stochastic three dimensional navier-stokes-∝ Stochastic three dimensional leray-∝ model UCTD Thesis (PhD)--University of Pretoria, 2010. In this thesis, we investigate the stochastic three dimensional Navier-Stokes-∝ model and the stochastic three dimensional Leray-∝ model which arise in the modelling of turbulent flows of fluids. We prove the existence of probabilistic weak solutions for the stochastic three dimensional Navier-Stokes-∝ model. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. We also discuss the uniqueness. The proof of the existence combines the Galerkin approximation and the compactness method. We also study the asymptotic behavior of weak solutions to the stochastic three dimensional Navier-Stokes-∝ model as ∝ approaches zero in the case of periodic box. Our result provides a new construction of the weak solutions for the stochastic three dimensional Navier-Stokes equations as approximations by sequences of solutions of the stochastic three dimensional Navier-Stokes-∝ model. Finally, we prove the existence and uniqueness of strong solution to the stochastic three dimensional Leray-∝ equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation combines with the weak convergence methods. We also study the asymptotic behavior of the strong solution as alpha goes to zero. We show that a sequence of strong solution converges in appropriate topologies to weak solutions of the stochastic three dimensional Navier-Stokes equations. All the results in this thesis are new and extend works done by several leading experts in both deterministic and stochastic models of fluid dynamics. Mathematics and Applied Mathematics unrestricted 2013-09-06T22:27:52Z 2011-06-23 2013-09-06T22:27:52Z 2011-04-05 2010 2011-06-16 Thesis Deugoue, G 2010, Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/25566 > D11/395/ag http://hdl.handle.net/2263/25566 http://upetd.up.ac.za/thesis/available/etd-06162011-055842/ © 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 University of Pretoria |
| spellingShingle | Stochastic three dimensional navier-stokes-∝ Stochastic three dimensional leray-∝ model UCTD Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations |
| title | Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations |
| title_full | Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations |
| title_fullStr | Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations |
| title_full_unstemmed | Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations |
| title_short | Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations |
| title_sort | existence of solutions for stochastic navier stokes alpha and leray alpha models of fluid turbulence and their relations to the stochastic navier stokes equations |
| topic | Stochastic three dimensional navier-stokes-∝ Stochastic three dimensional leray-∝ model UCTD |
| url | http://hdl.handle.net/2263/25566 http://upetd.up.ac.za/thesis/available/etd-06162011-055842/ |