Abstract for the talk on 24.04.2018 (16:45 h)Oberseminar ANALYSIS - PROBABILITY
Toan T. Nguyen (Pennsylvania State University)
L-infinity instability of Prandtl's layers
24.04.2018, 16:45 h, MPI für Mathematik in den Naturwissenschaften Leipzig, A3 01 (Sophus-Lie-SR)
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∞.
In this talk, I will present a recent joint work with E. Grenier (ENS Lyon), proving that, for a class of regular solutions of Navier Stokes equations, namely for shear proﬁles that are unstable to Rayleigh equations, this Prandtl’s Ansatz is false. In addition, for shear proﬁles that are monotone and stable to Rayleigh equations, the Prandtl’s asymptotic expansions are invalid.