This paper is devoted to the well-posedness of the stationary
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 Gérard-Varet and
Masmoudi, the general strategy is to reduce the problem to a bumpy channel
bounded in the vertical direction thanks to 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 .