The aim of this paper (arXiv:1705.04672), with E. Grenier, is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: . In his CPAM2000 paper, Grenier proved that there exists no Prandtl’s asymptotic expansion involving one Prandtl’s boundary layer with thickness of order , which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order . In this paper, we point out how the stability of the classical Prandtl’s layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in . That is, either the Prandtl’s layer or the boundary sublayer is nonlinearly unstable in the sup norm.

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