In 1904, Prandtl introduced his famous boundary layer theory in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to . His Ansatz was that the solution of Navier Stokes equations can be described as a solution of Euler equations, plus a boundary layer corrector, plus a vanishing error term in in the inviscid limit. In this post, I briefly announce my recent work with E. Grenier (ENS Lyon) on the Prandtl’s boundary layer theory, where we prove

- the Prandtl’s Ansatz is false for shear profiles that are unstable to Rayleigh equations;
- the Prandtl’s asymptotic expansion is invalid for shear profiles that are monotone and stable to Rayleigh equations.