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Seminario prelectura de tesis
SEMINARIO PRELECTURA DE TESIS
Diego Alonso Orán
(UAM-ICMAT)
"Regularity results for some models in geophysical fluid dynamics"
Director tesis: Antonio Córdoba Barba
Martes 19 de febrero de 2019
Módulo 17, aula 520
12:00 horas
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.
1
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.
1
Location Martes 19 de febrero de 2019 Módulo 17, aula 520 12:00 horas