Article
| Title: | The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in $L^r$-framework (English) |
| Author: | Neustupa, Tomáš |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 171-190 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | Stokes problem |
| Keyword: | artificial boundary condition |
| Keyword: | maximum regularity property |
| MSC: | 35Q30 |
| MSC: | 76D03 |
| MSC: | 76D05 |
| idZBL: | Zbl 07675565 |
| idMR: | MR4574652 |
| DOI: | 10.21136/AM.2022.0123-21 |
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| Date available: | 2023-03-31T09:34:59Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151611 |
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