Analysis of Fluids and Related Topics: Vortex sheets in domains with boundary

In this talk we consider the vanishing viscosity problem for incompressible fluid flow in a smooth, bounded domain. We are particularly concerned with the shear layer occurring near the boundary, a phenomenon which we explore in a few examples of flows with symmetry. We use this discussion as motivation for a framework for weak solutions of the inviscid equations which allow for exchange between circulation around the boundary and vorticity in the bulk of the fluid.