Applied Mathematics Colloquium/DE Seminar

Abstract: In this talk we discuss boundary layers, both as a physical phenomenon associated with the interaction of fluid flow with a wall, and as a mathematical consequence of the discrepancy between the boundary conditions associated with slightly viscous flow and inviscid flow. We focus our discussion on Kato's criterion, which provides a surprising condition for the vanishing viscosity limit to give rise to a smooth solution of the inviscid equations. We examine Kato's proof in detail, present some current extensions of Kato's argument and propose some open problems. ​