Boundary layers for the subcritical modes of the 3D primitive equations in a cube

In this article we study the boundary layers for the subcritical modes of the viscous Linearized Primitive Equations (LPEs) in a cube at small viscosity. The boundary layers include the parabolic boundary layers, ordinary boundary layers, and their interaction-corner layers. The boundary layer correctors are determined by a phenomenological study reminiscent of the Prandtl corrector approach and then a rigorous convergence result is proved which a posteriori justifies the phenomenological study.