Article
| Title: | On the Navier-Stokes equations with anisotropic wall slip conditions (English) |
| Author: | Le Roux, Christiaan |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 1-14 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This article deals with the solvability of the boundary-value problem for the Navier-Stokes equations with a direction-dependent Navier type slip boundary condition in a bounded domain. Such problems arise when steady flows of fluids in domains with rough boundaries are approximated as flows in domains with smooth boundaries. It is proved by means of the Galerkin method that the boundary-value problem has a unique weak solution when the body force and the variability of the surface friction are sufficiently small compared to the viscosity and the surface friction. (English) |
| Keyword: | Navier-Stokes equations |
| Keyword: | Stokes equations |
| Keyword: | rough boundary |
| Keyword: | slip boundary condition |
| MSC: | 76D03 |
| MSC: | 76D05 |
| MSC: | 76D07 |
| idZBL: | Zbl 07655736 |
| idMR: | MR4541072 |
| DOI: | 10.21136/AM.2021.0079-21 |
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| Date available: | 2023-02-03T11:00:04Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151491 |
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| Reference: | [3] Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems.Springer Monographs in Mathematics. Springer, New York (2011). Zbl 1245.35002, MR 2808162, 10.1007/978-0-387-09620-9 |
| Reference: | [4] Kamrin, K., Bazant, M. Z., Stone, H. A.: Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor.J. Fluid Mech. 658 (2010), 409-437. Zbl 1205.76080, MR 2678317, 10.1017/S0022112010001801 |
| Reference: | [5] Roux, C. Le: Flows of incompressible viscous liquids with anisotropic wall slip.J. Math. Anal. Appl. 465 (2018), 723-730. Zbl 1444.76047, MR 3809326, 10.1016/j.jmaa.2018.05.020 |
| Reference: | [6] Miranda, C.: Un'osservazione su un teorema di Brouwer.Boll. Unione Mat. Ital., II. Ser. 3 (1940), 5-7 Italian. Zbl 0024.02203, MR 0004775 |
| Reference: | [7] Showalter, R. E.: Hilbert Space Methods for Partial Differential Equations.Monographs and Studies in Mathematics 1. Pitman, London (1977). Zbl 0364.35001, MR 0477394 |
| Reference: | [8] Zampogna, G. A., Magnaudet, J., Bottaro, A.: Generalized slip condition over rough surfaces.J. Fluid Mech. 858 (2019), 407-436. Zbl 1415.76224, MR 3873518, 10.1017/jfm.2018.780 |
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