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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.05792 |
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| _version_ | 1866916118517514240 |
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| author | Mikhailov, Sergey E. |
| author_facet | Mikhailov, Sergey E. |
| contents | 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 with the basis constituted by the eigenfunctions of the periodic Bessel-potential operator, we prove the existence of a global weak solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: I. Existence Mikhailov, Sergey E. Analysis of PDEs 35A1, 35B10, 35K45, 35Q30, 76D05 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 with the basis constituted by the eigenfunctions of the periodic Bessel-potential operator, we prove the existence of a global weak solution. |
| title | Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: I. Existence |
| topic | Analysis of PDEs 35A1, 35B10, 35K45, 35Q30, 76D05 |
| url | https://arxiv.org/abs/2402.05792 |