Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis
Thesis (PhD)--University of Pretoria, 2016.
Saved in:
| Other Authors: | |
|---|---|
| Format: | Thesis |
| Language: | English |
| Published: |
University of Pretoria
2017
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613727474319360 |
|---|---|
| access_status_str | Open Access |
| author2 | Sango, Mamadou |
| author_browse | Sango, Mamadou |
| author_facet | Sango, Mamadou |
| collection | Thesis |
| dc_rights_str_mv | © 2017 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, 2016. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/60865 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:40:44.617Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| 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:2263/60865 Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis Sango, Mamadou u13214030@tuks.co.za Tegegn, Tesfalem Abate UCTD Thesis (PhD)--University of Pretoria, 2016. This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) turbulence flows. Part I consists of introduction and background (or preliminary) materials which were crucially important in the process. The main body of the thesis is included in parts II and III. In Part II, new regularity results for stochastic heat equations in probabilistic evolution spaces of Besov type are established, which in turn were used to establish global and local in time existence and uniqueness results for stochastic MHD equations. The existence result holds with positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools, such as Littlewood-Paley decomposition, Jean-Micheal Bony paradifferential calculus and stochastic calculus. Our global existence result is new in three-dimensional spaces and is published in [148](Sango and Tegegn, Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces, International Journal of Modern Physics B, World Scientific, 2016, 30). Our results in this part are novel; they introduced Littlewood-Paley theory and paradifferential calculus for stochastic partial differential equation. In Part III, we studied Kolmogorov's spectral theory for MHD equations with reasonably smooth external forces applied to both velocity and magnetic fields. Mathematics and Applied Mathematics PhD Unrestricted 2017-06-05T12:12:34Z 2017-06-05T12:12:34Z 2017-04-21 2016 Thesis Tegegn, TA 2016, Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis, PhD Thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/60865> A2017 http://hdl.handle.net/2263/60865 en © 2017 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 Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| title | Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| title_full | Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| title_fullStr | Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| title_full_unstemmed | Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| title_short | Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| title_sort | magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis |
| topic | UCTD |
| url | http://hdl.handle.net/2263/60865 |