Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis

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dc.contributor.advisor Sango, Mamadou en
dc.contributor.postgraduate Tegegn, Tesfalem Abate en
dc.date.accessioned 2017-06-05T12:12:34Z
dc.date.available 2017-06-05T12:12:34Z
dc.date.created 2017-04-21 en
dc.date.issued 2017 en
dc.description Thesis (PhD)--University of Pretoria, 2017. en
dc.description.abstract 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. en_ZA
dc.description.availability Unrestricted en
dc.description.degree PhD en
dc.description.department Mathematics and Applied Mathematics en
dc.identifier.citation Tegegn, TA 2017, 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> en
dc.identifier.other A2017 en
dc.identifier.uri http://hdl.handle.net/2263/60865
dc.language.iso en en
dc.publisher University of Pretoria en
dc.rights © 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. en
dc.subject UCTD en
dc.title Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis en
dc.type Thesis en


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