We investigate the behaviour of rotating incompressible flows near a nonflat
horizontal bottom. In the flat case, the velocity profile is given explicitly by a simple
linear ODE. When bottom variations are taken into account, it is governed by a
nonlinear PDE system, with far less obvious mathematical properties. We establish
the well-posedness of this system and the asymptotic behaviour of the solution away
from the boundary. In the course of the proof, we investigate in particular
the action of pseudodifferential operators in nonlocalized Sobolev spaces.
Our results extend an older paper of Gérard-Varet (J. Math. Pures Appl.82:11
(2003), 1453–1498), restricted to periodic variations of the bottom, using the
recent linear analysis of Dalibard and Prange (Anal. & PDE7:6 (2014),
1253–1315).