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

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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 Γin (the inflow) and Γ0 (boundary of the profile) and an artificial “do nothing”-type boundary condition on Γout (the outflow). We show that the considered problem has a strong solution with the Γr-maximum regularity property for appropriately integrable given data. From this we deduce a series of properties of the corresponding strong Stokes operator.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35, Praha 2, Czech Republic

    Tomáš Neustupa

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  1. Tomáš Neustupa
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Correspondence to Tomáš Neustupa.

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The research has been supported by European Regional Development Fund-Project “Center for Advanced Applied Science” No. CZ.02.1.01/0.0/0.0/16_019/0000778.

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Neustupa, T. The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in Lr-framework. Appl Math 68, 171–190 (2022). https://doi.org/10.21136/AM.2022.0123-21

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