  This paper is devoted to the well-posedness of the stationary $3$d
Stokes-Coriolis system set in a half-space with rough bottom and Dirichlet data
which does not decrease at space infinity. Our system is a linearized version
of the Ekman boundary layer system. We look for a solution of infinite energy
in a space of Sobolev regularity. Following an idea of G\'erard-Varet and
Masmoudi, the general strategy is to reduce the problem to a bumpy channel
bounded in the vertical direction thanks a transparent boundary condition
involving a Dirichlet to Neumann operator. Our analysis emphasizes some strong
singularities of the Stokes-Coriolis operator at low tangential frequencies.
One of the main features of our work lies in the definition of a Dirichlet to
Neumann operator for the Stokes-Coriolis system with data in the Kato space
$H^{1/2}_{uloc}$.
