  We study the weak steady Stokes problem, associated with a flow of a
Newtonian incompressible fluid through a spatially periodic profile cascade, in
the Lr-framework. The used mathematical model is based on the reduction to one
spatial period, represented by a bounded 2D domain Omega. The corresponding
Stokes problem is formulated by means of three types of boundary conditions:
the conditions of periodicity on the "lower" and "upper" parts of the boundary,
the Dirichlet boundary conditions on the "inflow" and on the profile and an
artificial "do nothing"--type boundary condition on the "outflow". Under
appropriate assumptions on the given data, we prove the existence and
uniqueness of a weak solution in W^{1,r}(Omega) and its continuous dependence
on the data. We explain the sense in which the "do nothing" boundary condition
on the "outflow" is satisfied.
