Ημερομηνία: Παρασκευη 11 Οκτωβρίου 2024
Ώρα: 15:00
Τόπος: Α22
Oμιλητής: Professor Ioannis Giannoulis, (University of Ioannina, Greece)
Τίτλος: The semi-geostrophic equations and their relation to the Euler equations
Περίληψη:The semi-geostrophic equations are two- or three-dimensional models that have been proposed in the 1970s as reduced models describing the large scale dynamics of weather fronts, based on the observation that these dynamics are determined mainly by the horizontal action of the Coriolis force arising from the rotation of the Earth around its axis.
In their so called dual formulation, that is, after a suitable change of variables, the semi-geostrophic equations can be expressed as a coupled system of a scalar nonlinear transport equation with a velocity field that is determined through the solution of a Monge-Amp\`ere equation which has the transported quantity as its right hand side. The existence of global in time weak solutions for this dual formulation has been proved by Benamou and Brenier in 1998. Later on, Loeper proved in 2006 the well-posedness of H\”older continuous solutions locally in time and showed that the dual semi-geostrophic equation in two dimensions can be seen as a perturbation of the Euler vorticity equation. In our talk we will focus on this latter relation and present results concerning its generalization and improved quantification, which have been obtained jointly with V. Kalivopoulos within a project funded by HFRI.