dc.contributor.advisor | Latushkin, Yuri, 1956- | eng |
dc.contributor.author | Vasudevan, Shibi Kapisthalam, 1984- | eng |
dc.date.issued | 2017 | eng |
dc.date.submitted | 2017 Summer | eng |
dc.description.abstract | We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u [times] [del.])u in the classical Euler equations of inviscid incompressible fluid by the term (v [times] [del.])u, where v is the regularized velocity satisfying (1 -[alpha]2[delta])v [equals] u, and [alpha] [greater than] 0. In the first part of the thesis, for the a-model, we develop analogues of the classical Arnol'd type stability criteria based on the energy-Casimir method for several settings including multi connected domains, periodic channels, and others. In the second part of the thesis, we study stability of a particular steady state, the unidirectional solution of the a-Euler equation on the two dimensional torus, having only one non zero mode in its Fourier decomposition. Using continued fractions, we give a proof of instability of the steady state under fairly general conditions. In the third part of the thesis we study various properties of a family of elliptic operators introduced by Zhiwu Lin in his work on instability of steady state solutions of the two dimensional Euler equations. This involves Birman-Schwinger type operators associated with the linearization of the Euler equations about the steady state and certain perturbation determinants. | eng |
dc.description.bibref | Includes bibliographical references (pages 159-164). | eng |
dc.description.statementofresponsibility | Dr. Yuri Latushkin, Dissertation Supervisor.|Includes vita. | eng |
dc.format.extent | 1 online resource (v, 165 pages) | eng |
dc.identifier.merlin | b121367113 | eng |
dc.identifier.oclc | 1023037937 | eng |
dc.identifier.uri | https://hdl.handle.net/10355/62340 | |
dc.identifier.uri | https://doi.org/10.32469/10355/62340 | eng |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartofcommunity | University of Missouri--Columbia. Graduate School. Theses and Dissertations | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | eng |
dc.title | Stability and instability results for the 2D [alpha]-Euler equations / | eng |
dc.title.alternative | Stability and instability results for the two dimensional a-Euler equations | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Doctoral | eng |
thesis.degree.name | Ph. D. | eng |