Speaker
Description
The Prandtl boundary layer theory has influenced many scientific disciplines, from aerodynamics to rheology. Analytically, it is nowadays widely recognized that the Prandtl equations are ill-posed in Sobolev spaces, even near certain shear flows, unless additional structural assumptions of monotonicity are imposed. However, they are well-posed in Gevrey class 2 spaces and whether well-posedness or ill-posedness holds in spaces between Sobolev and Gevrey class 2 remains an open problem. This talk presents a recent result, in collaboration with Joshua Kortum (University of Würzburg), which constructs a suitable family of explicit solutions to the Prandtl equations around a quadratic shear flow. These solutions are derived using a formula based on hypergeometric functions, allowing for direct classification of those exhibiting a dispersion relation of Gevrey class 2 type. Due to the explicit formulation, we further establish a result on the ill-posedness of the Prandtl equations within certain weigthed Gevrey classes.
