Appears in collection : Jean-Morlet Chair 2022 - Research School: Mathematical Advances in Geophysical Flows / Chaire Jean-Morlet 2022 - Ecole : Avancées mathématiques dans les flux géophysiques

The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance a convection term to the previous examples. Eventually, we will introduce some tools for the study of the Prandtl equation.