Appears in collection : 2026 - T2 - WS1 - Vortices and vorticity in geophysical flows

The question of the stability of the boundary layers which appear as the viscosity of the fluid goes to zero is a classical question in Fluid Mechanics. In this talk I will discuss recent mathematical results on this question and in particular show that any shear layer is linearly and nonlinearly unstable provided the viscosity is small enough, and that the classical Prandtl boundary layers are always unstable.