A journey into the realm of stratified fluids
Abstract
I will propose a gentle introduction to the mathematical analysis of inviscid stratified fluids, of importance in oceanography. The focus will be on the so-called Euler-Boussinesq system, that is a widely used toy model. I will mainly discuss some of the challenges arising in two asymptotic regimes for these equations: the long-time behaviour and the hydrostatic limit. I will try to highlight some links with dispersive equations, kinetic theory, spectral theory, etc...