On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
We study a mathematical model describing steady creeping flows of a non-uniformly heated incompressible fluid through a bounded 3D domain with locally Lipschitz boundary. The model under consideration is a system of second-order nonlinear partial differential equations with mixed boundary conditions...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2019-09-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20621/16868 |
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| author | Anastasia Aleksandrovna Domnich Evgenii Sergeevich Baranovskii Mikhail Anatolievich Artemov |
| author_facet | Anastasia Aleksandrovna Domnich Evgenii Sergeevich Baranovskii Mikhail Anatolievich Artemov |
| author_sort | Anastasia Aleksandrovna Domnich |
| collection | DOAJ |
| description | We study a mathematical model describing steady creeping flows of a non-uniformly heated incompressible fluid through a bounded 3D domain with locally Lipschitz boundary. The model under consideration is a system of second-order nonlinear partial differential equations with mixed boundary conditions. On in-flow and out-flow parts of the boundary the pressure, the temperature and the tangential component of the velocity field are prescribed, while on impermeable solid walls the no-slip condition and a Robin-type condition for the temperature are used. For this boundary-value problem, we introduce the concept of a weak solution (a pair “velocity-temperature”), which is defined as a solution to some system of integral equations. The main result of the work is a theorem on the existence of weak solutions in a subspace of the Cartesian product of two Sobolev's spaces. To prove this theorem, we give an operator interpretation of the boundary value problem, derive a priori estimates of solutions, and apply the Leray-Schauder fixed point theorem. Moreover, energy equalities are established for weak solutions. |
| first_indexed | 2024-04-13T15:56:32Z |
| format | Article |
| id | doaj.art-ae2b654cd28d440093fafe985f9094dd |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:56:32Z |
| publishDate | 2019-09-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-ae2b654cd28d440093fafe985f9094dd2022-12-22T02:40:41ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812019-09-0123341742910.14498/vsgtu171318041On a mathematical model of non-isothermal creeping flows of a fluid through a given domainAnastasia Aleksandrovna Domnich0Evgenii Sergeevich Baranovskii1Mikhail Anatolievich Artemov2Russian Air Force Military Educational and Scientific Center of the "N. E. Zhukovskiy and Yu. A. Gagarin Air Force Academy"Voronezh State University, Faculty of Applied Mathematics, Informatics and MechanicsVoronezh State University, Faculty of Applied Mathematics, Informatics and MechanicsWe study a mathematical model describing steady creeping flows of a non-uniformly heated incompressible fluid through a bounded 3D domain with locally Lipschitz boundary. The model under consideration is a system of second-order nonlinear partial differential equations with mixed boundary conditions. On in-flow and out-flow parts of the boundary the pressure, the temperature and the tangential component of the velocity field are prescribed, while on impermeable solid walls the no-slip condition and a Robin-type condition for the temperature are used. For this boundary-value problem, we introduce the concept of a weak solution (a pair “velocity-temperature”), which is defined as a solution to some system of integral equations. The main result of the work is a theorem on the existence of weak solutions in a subspace of the Cartesian product of two Sobolev's spaces. To prove this theorem, we give an operator interpretation of the boundary value problem, derive a priori estimates of solutions, and apply the Leray-Schauder fixed point theorem. Moreover, energy equalities are established for weak solutions.https://journals.eco-vector.com/1991-8615/article/viewFile/20621/16868flux problemnon-isothermal flowscreeping flowsmixed boundary conditionsweak solutions |
| spellingShingle | Anastasia Aleksandrovna Domnich Evgenii Sergeevich Baranovskii Mikhail Anatolievich Artemov On a mathematical model of non-isothermal creeping flows of a fluid through a given domain Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki flux problem non-isothermal flows creeping flows mixed boundary conditions weak solutions |
| title | On a mathematical model of non-isothermal creeping flows of a fluid through a given domain |
| title_full | On a mathematical model of non-isothermal creeping flows of a fluid through a given domain |
| title_fullStr | On a mathematical model of non-isothermal creeping flows of a fluid through a given domain |
| title_full_unstemmed | On a mathematical model of non-isothermal creeping flows of a fluid through a given domain |
| title_short | On a mathematical model of non-isothermal creeping flows of a fluid through a given domain |
| title_sort | on a mathematical model of non isothermal creeping flows of a fluid through a given domain |
| topic | flux problem non-isothermal flows creeping flows mixed boundary conditions weak solutions |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20621/16868 |
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