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http://bura.brunel.ac.uk/handle/2438/31420| Title: | Spatially Periodic Solutions for Evolution Anisotropic Variable‐Coefficient Navier–Stokes Equations: II. Serrin‐Type Solutions |
| Authors: | Mikhailov, SE |
| Keywords: | anisotropic Navier-Stokes equations;evolution Navier–Stokes equations;partial differential equations;relaxed ellipticity condition;Serrin-type solutions;spatially periodic solutions;variable coefficients |
| Issue Date: | 4-Jun-2025 |
| Publisher: | Wiley |
| Citation: | Mikhailov, S.E. (2025) 'Spatially Periodic Solutions for Evolution Anisotropic Variable‐Coefficient Navier–Stokes Equations: II. Serrin‐Type Solutions', Mathematical Methods in the Applied Sciences, 2025, 0 (ahead of print), pp. 1 - 28. doi: 10.1002/mma.10921. |
| Abstract: | We consider evolution (non-stationary) space-periodic solutions to the n-dimensional non-linear Navier-Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm, we prove the existence of Serrin-type solutions, that is, weak solutions with the velocity in the periodic space L2(0,T;H˙n/2#σ), n≥2. The solution uniqueness and regularity results are also discussed. |
| Description: | Data Availability Statement: This paper has no associated data. |
| URI: | https://bura.brunel.ac.uk/handle/2438/31420 |
| DOI: | https://doi.org/10.1002/mma.10921 |
| ISSN: | 0170-4214 |
| Other Identifiers: | ORCiD: Sergey E. Mikhailov https://orcid.org/0000-0002-3268-9290 |
| Appears in Collections: | Dept of Mathematics Research Papers |
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|---|---|---|---|---|
| FullText.pdf | Copyright © 2025 The Author(s). 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 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited. | 1.37 MB | Adobe PDF | View/Open |
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