Regularity results for some models in geophysical fluid dynamics
Author
Alonso Orán, DiegoAdvisor
Cordoba Barba, AntonioEntity
UAM. Departamento de MatemáticasDate
2019-04-12Funded by
This thesis has been funded by a Severo Ochoa FPI scholarship for Centres of Excellence in R&D (SEV-2015-0554) and by the grant MTM2017-83496-P from the Spanish Ministry of Economy and Competitiveness.Subjects
Dinámica de fluidos - Tesis doctorales; MatemáticasNote
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 12-04-2019Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
This thesis centers on the study of two di erent problems of partial
di erential equations arising from geophysics and
uid mechanics: the
surface quasi-geostrophic equation and the so called, Incompressible
Slice Model.
The surface quasi-geostrophic equation is a two dimensional nonlo-
cal partial di erential equation of geophysical importance, describing
the evolution of a surface buoyancy in a rapidly rotating, strati ed
potential vorticity
uid. In the rst part of the talk, we will present
some global regularity results for its dissipative analogue in the critical
regime for the two dimensional sphere.
After that, we will introduce the Incompressible Slice Model deal-
ing with oceanic and atmospheric
uid motions taking place in a ver-
tical slice domain
R2, with smooth boundary. The ISM can
be understood as a toy model for the full 3D Euler-Boussinesq equa-
tions. We will study the solution properties of the Incompressible Slice
Model: characterizing a class of equilibrium solutions, establishing the
local existence of solutions and providing a blow-up criterion.
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