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| Boundary layers typically appear in the inviscid limit of the Navier-Stokes equations. There are ranges of spatial frequencies and large Reynolds number with which generic boundary layers are spectrally unstable. This includes boundary layers without an inflection point, and thus the instability is due to the presence of viscosity. I will introduce a new, operator-based approach to construct exact growing modes of the linearized Navier-Stokes about stationary boundary layers. Our approach avoids to deal with matching inner and outer asymptotic expansions, but instead involves a careful study of singularity in the critical layers by deriving pointwise bounds on the Green function of the corresponding Rayleigh and Airy operators. This is a joint work with Grenier and Guo. |
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