This thesis is devoted to the motion of the incompressible and inviscid flow which is ax-
isymmetric and swirl-free in a cylinder, where the hydrostatic approximation is made in the
axial direction. It addresses the problem of local existence and uniqueness in the spaces of
analytic functions for the Cauchy problem for the inviscid primitive equations, also called the
hydrostatic incompressible Euler equations, on a cylinder, under some extra conditions. Following the method introduced by Kukavica-Temam-Vicol-Ziane in Int. J. Differ. Equ. 250
(2011) , we use the suitable extension of the Cauchy-Kowalewski theorem to construct locally in
time, unique and real-analytic solution, and find the explicit rate of decay of the radius of real-analiticity. Furthermore, this thesis discusses the problem of finite-time blowup of the solution
of the system of equations. Following a part of the method introduced by Wong in Proc Am
Math Soc. 143 (2015), we prove that the first derivative of the radial velocity blows up in time,
using primary functional analysis tools for a certain class of initial data. Taking the solution
frozen at r = 0, we can apply an a priori estimate on the second derivative of the pressure term,
to derive a Ricatti type inequality. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/13932 |
| Date | 02 May 2022 |
| Creators | SadatHosseiniKhajouei, Narges |
| Contributors | Ibrahim, Slim, Goluskin, David |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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