Reynolds Stress Tensor Systems and Applications to Nonuniqueness of Weak Solutions to Fluid

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/z316q7803

Descriptions

Attribute Name	Values
Creator	Donaghue, Patrick E.
Abstract	In the 1954 John Nash [1] showed, through use of an iterative scheme of approximate embedding maps, that the sphere S² could be isometrically embedded into a ball of any radius by a C¹ map. In the 1980's M. Gromov [2] generalized Nash's work to the h-principal and convex integration. Recent research in fluid dynamics has used analogs to convex integration schemes to demonstrate nonuniqueness of weak solutions to both Euler and Navier-Stokes equations. In this paper we examine recent work by DeLellis and Székelyhidi Jr. [3] as well as Buckmaster and Vicol [4] on the nonuniqueness of Fluid Dynamics equations. Specifically we focus on solution to Reynolds Stress system which act as approximate solutions to Euler and Navier-Stokes equation. We also develop basic properties of the Dirichlet kernel used in the construction of intermittent Beltrami flows.
License	All rights reserved
Resource Type	Masters Thesis
Date Issued	2019-08-15
Degree Level	Master's
Degree Name	Master of Science (M.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2020
Advisor	Thomann, Enrique
Committee Member	Finch, David Schmittner, Andreas Cozzi, Elaine
Academic Affiliation	Mathematics
Déclaration de droits	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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