Strong Solutions of the Incompressible Navier–Stokes–Voigt Model
This paper deals with an initial-boundary value problem for the Navier−Stokes−Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/2/181 |
| _version_ | 1818986394722238464 |
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| author | Evgenii S. Baranovskii |
| author_facet | Evgenii S. Baranovskii |
| author_sort | Evgenii S. Baranovskii |
| collection | DOAJ |
| description | This paper deals with an initial-boundary value problem for the Navier−Stokes−Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo−Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative. |
| first_indexed | 2024-12-20T18:50:06Z |
| format | Article |
| id | doaj.art-be86b0bfe2894788b5d092a9a3d65506 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T18:50:06Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-be86b0bfe2894788b5d092a9a3d655062022-12-21T19:29:37ZengMDPI AGMathematics2227-73902020-02-018218110.3390/math8020181math8020181Strong Solutions of the Incompressible Navier–Stokes–Voigt ModelEvgenii S. Baranovskii0Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, RussiaThis paper deals with an initial-boundary value problem for the Navier−Stokes−Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo−Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.https://www.mdpi.com/2227-7390/8/2/181navier–stokes–voigt equationsviscoelastic modelsnon-newtonian fluidstrong solutionsexistence and uniqueness theoremfaedo–galerkin approximationsstokes operatorlong-time behavior |
| spellingShingle | Evgenii S. Baranovskii Strong Solutions of the Incompressible Navier–Stokes–Voigt Model Mathematics navier–stokes–voigt equations viscoelastic models non-newtonian fluid strong solutions existence and uniqueness theorem faedo–galerkin approximations stokes operator long-time behavior |
| title | Strong Solutions of the Incompressible Navier–Stokes–Voigt Model |
| title_full | Strong Solutions of the Incompressible Navier–Stokes–Voigt Model |
| title_fullStr | Strong Solutions of the Incompressible Navier–Stokes–Voigt Model |
| title_full_unstemmed | Strong Solutions of the Incompressible Navier–Stokes–Voigt Model |
| title_short | Strong Solutions of the Incompressible Navier–Stokes–Voigt Model |
| title_sort | strong solutions of the incompressible navier stokes voigt model |
| topic | navier–stokes–voigt equations viscoelastic models non-newtonian fluid strong solutions existence and uniqueness theorem faedo–galerkin approximations stokes operator long-time behavior |
| url | https://www.mdpi.com/2227-7390/8/2/181 |
| work_keys_str_mv | AT evgeniisbaranovskii strongsolutionsoftheincompressiblenavierstokesvoigtmodel |