It is well known that, for fast rotating fluids with the axis of rotation being perpendicular
to the boundary, the boundary layer is of Ekman-type, described by a linear ODE
system. In this talk, we consider fast rotating fluids, with the axis of rotation being par-
allel to the boundary. We show that, for certain initial data, the corresponding boundary
layer can be described by a nonlinear, degenerated PDE system which is similar to the
2D Prandtl system. Finally, we prove the well-posedness of the governing system of the
boundary layer in the space of analytic functions with respect to tangential variable.
This is a joint work with Wei-Xi Li (Wuhan University, School of Mathematics and
Statistics) and Chao-Jiang Xu (Université de Rouen Normandie).