  The paper deals with the Stokes problem, associated with a flow of a viscous
incompressible fluid through a spatially periodic profile cascade. We use
results from [32] (the maximum regularity property in the $L^2$-framework) and
[33] (the weak solvability in $W^{1,r}$), and extend the findings on the
maximum regularity property to the general $L^r$-framework (for $1<r<\infty$).
Using the reduction to one spatial period $\Omega$, the problem is formulated
by means of boundary conditions of three types: the conditions of periodicity
on curves $\Gamma_0$ and $\Gamma_1$, the Dirichlet boundary conditions on
$\Gamma_{\rm in}$ and $\Gamma_P$ and an artificial "do nothing"-type boundary
condition on $\Gamma_{\rm out}$ (see Fig. 1). We show that, although domain
$\Omega$ is not smooth and different types of boundary conditions "meet" in the
vertices of $\partial\Omega$, the considered problem has a strong solution with
the maximum regularity property for "smooth" data. We explain the sense in
which the "do nothing" boundary condition is satisfied for both weak and strong
solutions.
