Title: On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows,
Abstract: In this paper, we study Prandtl's boundary layer asymptotic expansion for
incompressible fluids on the half-space in the inviscid limit. In \cite{Gr1},
E. Grenier proved that Prandtl's Ansatz is false for data with Sobolev
regularity near Rayleigh's unstable shear flows. In this paper, we show that
this Ansatz is also false for Rayleigh's stable shear flows. Namely we
construct unstable solutions near arbitrary stable monotonic boundary layer
profiles. Such shear flows are stable for Euler equations, but not for
Navier-Stokes equations: adding a small viscosity destabilizes the flow.