$L^\infty$ instability of Prandtl layers

$L^\infty$ instability of Prandtl layers

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Toan Nguyen, Pennsylvania State University
Fine Hall 322

In 1904, Prandtl introduced his famous boundary layer theory to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary in the inviscid limit. His Ansatz was that the solution of Navier Stokes can be described as a solution of Euler, plus a boundary layer corrector, plus a vanishing error term in $L^\infty$. In this talk, I will present a recent joint work with E. Grenier (ENS Lyon), proving that, for a class of explicit regular solutions of Navier Stokes equations, this Prandtl's Ansatz is wrong. Time permitting, I will briefly show that even near monotonic boundary layers, the Prandtl's asymptotic expansions are invalid.