In this talk, we will introduce the theory of the mathematical models for geophysical fluids like the atmosphere and the oceans. These fluids on large scales are characterized by a presence of a strong Coriolis force.
In this context, we will start explaining in detail a “toy-model” represented by the barotropic Navier-Stokes system in fast rotation. The main goal is to study the asymptotic behaviour of the system in the limit when the Coriolis force tends to infinity. To achieve this, we will present the main steps to tackle this kind of problems that, in general, are called “singular perturbation problems”. In the second part of the talk, we will show the results that we have obtained in a more complex case: the so-called Navier-Stokes-Fourier system, where the presence of external forces and the variation of temperature appear.
These last results are a part of a joint work with Daniele Del Santo, Francesco Fanelli and Aneta Wróblewska-Kamińska.