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## Green function for linearized Navier-Stokes around boundary layers: away from critical layers

I’ve just submitted this new paper with E. Grenier (ENS de Lyon) on arxiv (scheduled to announce next Tuesday 1:00GMT), in which we construct the Green function for the classical Orr-Sommerfeld equations and derive sharp semigroup bounds for linearized Navier-Stokes equations around a boundary layer profile. This is part of the long program to understand the stability of classical Prandtl’s layers appearing in the inviscid limit of incompressible Navier-Stokes flows.

\displaystyle \begin{aligned} \partial_tf + 2 \nu |k|^2 f \ = \ Q[f] \end{aligned}