On nonlinear instability of stable Prandtl’s boundary layers

Jeudi 22 juin 15:45-16:45 Toan Nguyen - Penn State University

Résumé : I shall present recent works with Emmanuel Grenier (ENS de Lyon) on studying Prandtl’s boundary layer asymptotic expansion for incompressible fluids on the half-space in the inviscid limit. Grenier proved in 2000 that Prandtl’s Ansatz is false for data with Sobolev regularity near Rayleigh’s unstable shear flows. In this work, we show that this Ansatz is also false for Rayleigh’s stable shear flows. Such flows are stable for Euler equations, but not for Navier-Stokes equations : adding a small viscosity destabilizes the flow.

Lieu : Bât 425, salle 113-115

On nonlinear instability of stable Prandtl’s boundary layers  Version PDF
juin 2017 :

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