Mathematical study of degenerate boundary layers
Anne-Laure Dalibard, Laure Saint‐Raymond · 2015
This paper is concerned with a complete asymptotic analysis as E \\to 0 of the Munk equation \\partial _x\\psi -E \\Delta ^2 \\psi = \\tau in a domain \\Omega \\subset \\mathbf R^2, supplemented with boundary conditions for \\psi and \\partial _n \\psi . This equation is a simple model for the circulation of currents in closed basins, the variables x and y being respectively the longitude and the latitude. A crude analysis shows that as E \\to 0, the weak limit of \\psi satisfies the so-called Sverdrup transport equation inside the domain, namely \\partial _x \\psi ^0=\\tau , while boundary layers appear in the vicinity of the boundary.