Boundary layers for the 2D linearized primitive equations
Makram Hamouda, Chang‐Yeol Jung, Roger Témam · Communications on Pure & Applied Analysis · 2008
In this article, we establish the asymptotic behavior, when theviscosity goes to zero, of the solutions of the Linearized PrimitiveEquations (LPEs) in space dimension $2$. More precisely, we provethat the LPEs solution behaves like the corresponding inviscidproblem solution inside the domain plus an explicit correctorfunction in the neighborhood of some parts of the boundary. Twocases are considered, the subcritical and supercritical modesdepending on the fact that the frequency mode is less or greaterthan the ratio between the reference stratified flow (around whichwe linearized) and the buoyancy frequency. The problem of boundarylayers for the LPEs is of a new type since the corresponding limitproblem displays a set of (unusual) nonlocal boundary conditions.