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http://bura.brunel.ac.uk/handle/2438/24969| Title: | Stationary anisotropic Stokes, Oseen and Navier–Stokes systems: Periodic solutions in ℝ<sup><i>n</i></sup> |
| Authors: | Mikhailov, SE |
| Keywords: | anisotropic Stokes, Oseen and Navier‐Stokes equations;existence;higher dimensions;periodic Sobolev spaces;uniqueness and regularity;relaxed ellipticity |
| Issue Date: | 13-Mar-2023 |
| Publisher: | Wiley |
| Citation: | Mikhailov, S.E. (2023) 'Stationary anisotropic Stokes, Oseen and Navier–Stokes systems: Periodic solutions in ℝ<sup><i>n</i></sup>', Mathematical Methods in the Applied Sciences, 46 (9), pp. 10903-10928. doi: 10.1002/mma.9159. |
| Abstract: | Copyright © 2023 The Authors. First, the solution uniqueness, existence and regularity for stationary anisotropic (linear) Stokes and generalised Oseen systems with constant viscosity coefficients in a compressible framework are analysed in a range of periodic Sobolev (Bessel-potential) spaces in ℝn. By the Galerkin algorithm and the Brower fixed point theorem, the existence of solution to the stationary anisotropic (nonlinear) Navier–Stokes incompressible system is shown in a periodic Sobolev space for any n ≥ 2. Then the solution uniqueness and regularity results for stationary anisotropic periodic Navier–Stokes system are established for n ∈ {2,3,4} . |
| URI: | https://bura.brunel.ac.uk/handle/2438/24969 |
| DOI: | https://doi.org/10.1002/mma.9159 |
| ISSN: | 0170-4214 |
| Other Identifiers: | ORCID iD: Sergey E. Mikhailov https://orcid.org/0000-0002-3268-9290 arXiv:2207.04532v1 |
| Appears in Collections: | Dept of Mathematics Research Papers |
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|---|---|---|---|---|
| FullText.pdf | Copyright © 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. | 636.8 kB | Adobe PDF | View/Open |
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