Mathematical Study of Degenerate Boundary Layers. - Dalibard, Anne-Laure (Memoirs of the American Mathematical Society Ser., 2018)
This paper is concerned with a complete asymptotic analysis as E → 0 of the Munk equation \partial _xψ -E Δ ^2 ψ = τ in a domain Ω \subset \mathbf R^2, supplemented with boundary conditions for ψ and \partial _n ψ . 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 → 0, the weak limit of ψ satisfies the so-called Sverdrup transport equation inside the domain, namely \partial _x ψ ^0=τ, while boundary layers appear in.