The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in Lr-framework

Abstract

We deal with the steady Stokes problem, associated with a flow of a viscous incompressible fluid through a spatially periodic profile cascade. Using the reduction to domain Ω, which represents one spatial period, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves Γ₋ and Γ₊ (lower and upper parts of ∂Ω), the Dirichlet boundary conditions on Γ_in (the inflow) and Γ₀ (boundary of the profile) and an artificial “do nothing”-type boundary condition on Γ_out (the outflow). We show that the considered problem has a strong solution with the Γ^r-maximum regularity property for appropriately integrable given data. From this we deduce a series of properties of the corresponding strong Stokes operator.