# The instability of classical boundary layers

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Toan Nguyen, Penn State/Princeton
Fine Hall 314

In this talk, I shall present two results concerning the validity of boundary layers that were introduced by Prandtl in 1904 as an Ansatz for slightly viscous Navier-Stokes flows near a boundary: Namely, (1) there are shear flows so that the classical Prandtl's Ansatz is false, and (2) even for monotone and convex shear flows which are spectrally stable to both Euler and Prandtl equations, they are nonlinearly unstable to Navier-Stokes and the classical Prandtl's boundary layer expansions also fail. These instabilities are estimated in sup norm, which is the weakest norm to measure boundary layers in the inviscid limit. This is joint work with Emmanuel Grenier from ENS Lyon.