Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results
This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in int...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/7/1300 |
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| author | Evgenii S. Baranovskii Vyacheslav V. Provotorov Mikhail A. Artemov Alexey P. Zhabko |
| author_facet | Evgenii S. Baranovskii Vyacheslav V. Provotorov Mikhail A. Artemov Alexey P. Zhabko |
| author_sort | Evgenii S. Baranovskii |
| collection | DOAJ |
| description | This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains. |
| first_indexed | 2024-03-10T09:21:01Z |
| format | Article |
| id | doaj.art-b078118b77634564acdffe6d2d262ad8 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T09:21:01Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b078118b77634564acdffe6d2d262ad82023-11-22T05:10:18ZengMDPI AGSymmetry2073-89942021-07-01137130010.3390/sym13071300Non-Isothermal Creeping Flows in a Pipeline Network: Existence ResultsEvgenii S. Baranovskii0Vyacheslav V. Provotorov1Mikhail A. Artemov2Alexey P. Zhabko3Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, RussiaDepartment of Mathematics, Voronezh State University, 394018 Voronezh, RussiaDepartment of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, RussiaDepartment of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, RussiaThis paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.https://www.mdpi.com/2073-8994/13/7/1300pipeline networknon-isothermal flowstemperature-dependent viscositypressure boundary conditionsweak solutionslarge-date existence |
| spellingShingle | Evgenii S. Baranovskii Vyacheslav V. Provotorov Mikhail A. Artemov Alexey P. Zhabko Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results Symmetry pipeline network non-isothermal flows temperature-dependent viscosity pressure boundary conditions weak solutions large-date existence |
| title | Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results |
| title_full | Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results |
| title_fullStr | Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results |
| title_full_unstemmed | Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results |
| title_short | Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results |
| title_sort | non isothermal creeping flows in a pipeline network existence results |
| topic | pipeline network non-isothermal flows temperature-dependent viscosity pressure boundary conditions weak solutions large-date existence |
| url | https://www.mdpi.com/2073-8994/13/7/1300 |
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