# Mathematical study of a degenerate boundary layer

# Mathematical study of a degenerate boundary layer

The goal of this talk is to analyze asymptotically an equation stemming from oceanographic models describing the motion of large scale currents. This equation is known to give rise to boundary layers on the east and west coasts of the domain. One of the major issues of our study lies in the fact that the size of these lateral boundary layers becomes very large as one approaches the north and south end points of the domain. In a neighbourhood of these zones, the classical construction of boundary layers must therefore be completely changed. We prove that the north and south boundary layers are the solutions of some evolutionary equation, and that their profile is thus non-intrinsic. We also exhibit discontinuity boundary layers, which penetrate the interior of the domain when the latter has islands, for instance. This is a joint work with Laure Saint-Raymond.