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We study the weak steady Stokes problem, associated with a flow of aNewtonian incompressible fluid through a spatially periodic profile cascade, inthe Lr-framework. The used mathematical model is based on the reduction to onespatial period, represented by a bounded 2D domain Omega. The correspondingStokes 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 anartificial "do nothing"--type boundary condition on the "outflow". Underappropriate assumptions on the given data, we prove the existence anduniqueness of a weak solution in W^{1,r}(Omega) and its continuous dependenceon the data. We explain the sense in which the "do nothing" boundary conditionon the "outflow" is satisfied.

The weak Stokes problem associated with a flow through a profile cascade in Lr-framework