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Title: | Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier–Stokes Equations: I. Weak Solution Existence |
Authors: | Mikhailov, SE |
Keywords: | partial differential equations;evolution Navier–Stokes equations;anisotropic Navier–Stokes equations;spatially periodic solutions;variable coefficients;relaxed ellipticity condition |
Issue Date: | 12-Jun-2024 |
Publisher: | MDPI |
Citation: | Mikhailov, S.E. (2024) 'Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier–Stokes Equations: I. Weak Solution Existence', Mathematics, 12 (12), 1817, pp. 1 - 27. doi: 10.3390/math12121817. |
Abstract: | We consider evolution (non-stationary) spatially-periodic solutions to the n-dimensional non-linear Navier–Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in spatial coordinates and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm with the basis constituted by the eigenfunctions of the periodic Bessel-potential operator, we prove the existence of a global weak solution. |
Description: | Data Availability Statement: This paper has no associated data. MSC: 35A1; 35B10; 35K45; 35Q30; 76D05. |
URI: | https://bura.brunel.ac.uk/handle/2438/29212 |
DOI: | https://doi.org/10.3390/math12121817 |
Other Identifiers: | ORCiD: Sergey E. Mikhailov https://orcid.org/0000-0002-3268-9290 1817 |
Appears in Collections: | Dept of Mathematics Research Papers |
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