Well-posedness and blowup results for the swirl-free and axisymmetric primitive equations in a cylinder

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.

Author dc:creator

• SadatHosseiniKhajouei, Narges

Advisors dc:contributor.supervisor

• Ibrahim, Slim
• Goluskin, David

• Primitive equations
• well-posedness
• blowup

Statement dc:rights

• Available to the World Wide Web

Language dc:language.iso

en, English

Handle dc:identifier.uri

http://hdl.handle.net/1828/13932

OAI record oai:identifier

https://dspace.library.uvic.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Adspace.library.uvic.ca%3A1828%2F13932