Also appears in collection : Jean-Morlet Chair 2022 - Research School: Mathematical Advances in Geophysical Flows / Chaire Jean-Morlet 2022 - Ecole : Avancées mathématiques dans les flux géophysiques

Many hydrodynamic instabilities take place near a solid boundary at high Reynolds number. This reflects into the mathematical theory of the classical Prandtl model for the boundary layer: it exhibits high frequency instabilities, limiting its well-posedness to infinite regularity (Gevrey) spaces. After reviewing shortly this fact, we will turn to the Triple Deck model, a refinement of the Prandtl system that is commonly accepted to be more stable. We will show that this is actually wrong, and that the recent result of analytic well-posedness obtained by Iyer and Vicol is more or less optimal. This is based on joint work with Helge Dietert.