Analysis of Fluids and Related Topics: L^\infty instability of Prandtl layers, Toan Nguyen, University of Pennsylvania

Speaker: Toan Nguyen, University of Pennsylvania

Abstract: 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∞L∞. 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.