| Abstrakt: |
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 $\Omega$, which represents one spatial period, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves $\Gamma_-$ and $\Gamma_+$ (lower and upper parts of $\partial\Omega$), the Dirichlet boundary conditions on $\Gamma_{\rm in}$ (the inflow) and $\Gamma_0$ (boundary of the profile) and an artificial "do nothing"-type boundary condition on $\Gamma_{\rm out}$ (the outflow). We show that the considered problem has a strong solution with the $L^r$-maximum regularity property for appropriately integrable given data. From this we deduce a series of properties of the corresponding strong Stokes operator. |
