Graduate Thesis Or Dissertation

 

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

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

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  • 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.
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