Boundary Layers and Applications to the Vanishing Viscosity Limit for Incompressible Fluids

The main goal of the course is to introduce the theory of boundary layers with emphasis on viscous boundary layers for incompressible flows, discussing some recent developments in the rigorous analysis of viscous boundary layers and the vanishing viscosity limit. We will first discuss the case of boundary layers for linear equations (ordinary differential equations and the Laplace equation), in order to present the topics in a context more familiar to the students, and then for fluids leading to Prandtl equation. We will provide the necessary tools to analyze more complex models and to let interested students study open problems from an analytic standpoint.