Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit
The main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under consideration is a boundary value problem for the s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Polymers |
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| Online Access: | https://www.mdpi.com/2073-4360/14/18/3789 |
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| author | Evgenii S. Baranovskii Mikhail A. Artemov |
| author_facet | Evgenii S. Baranovskii Mikhail A. Artemov |
| author_sort | Evgenii S. Baranovskii |
| collection | DOAJ |
| description | The main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under consideration is a boundary value problem for the system of strongly nonlinear partial differential equations of third order with the zero Dirichlet boundary condition. We propose the concept of a full weak solution (velocity–pressure pair) in the distributions sense. Using the method of introduction of auxiliary viscosity, the acute angle theorem for generalized monotone nonlinear operators, and the Krasnoselskii theorem on the continuity of the superposition operator in Lebesgue spaces, we obtain sufficient conditions for the existence of a full weak solution satisfying some energy inequality. Moreover, it is shown that the obtained solutions of the original problem converge to a solution of the steady-state damped Navier–Stokes system as the relaxation viscosity tends to zero. |
| first_indexed | 2024-03-09T22:45:49Z |
| format | Article |
| id | doaj.art-c434f52c8678415ab167b444212a75ae |
| institution | Directory Open Access Journal |
| issn | 2073-4360 |
| language | English |
| last_indexed | 2024-03-09T22:45:49Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Polymers |
| spelling | doaj.art-c434f52c8678415ab167b444212a75ae2023-11-23T18:29:56ZengMDPI AGPolymers2073-43602022-09-011418378910.3390/polym14183789Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation LimitEvgenii S. Baranovskii0Mikhail A. Artemov1Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, RussiaDepartment of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, RussiaThe main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under consideration is a boundary value problem for the system of strongly nonlinear partial differential equations of third order with the zero Dirichlet boundary condition. We propose the concept of a full weak solution (velocity–pressure pair) in the distributions sense. Using the method of introduction of auxiliary viscosity, the acute angle theorem for generalized monotone nonlinear operators, and the Krasnoselskii theorem on the continuity of the superposition operator in Lebesgue spaces, we obtain sufficient conditions for the existence of a full weak solution satisfying some energy inequality. Moreover, it is shown that the obtained solutions of the original problem converge to a solution of the steady-state damped Navier–Stokes system as the relaxation viscosity tends to zero.https://www.mdpi.com/2073-4360/14/18/3789non-Newtonian fluidaqueous polymer solutionsrelaxation viscositydampingnonlinear partial differential equationsfull weak solution |
| spellingShingle | Evgenii S. Baranovskii Mikhail A. Artemov Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit Polymers non-Newtonian fluid aqueous polymer solutions relaxation viscosity damping nonlinear partial differential equations full weak solution |
| title | Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit |
| title_full | Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit |
| title_fullStr | Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit |
| title_full_unstemmed | Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit |
| title_short | Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit |
| title_sort | model for aqueous polymer solutions with damping term solvability and vanishing relaxation limit |
| topic | non-Newtonian fluid aqueous polymer solutions relaxation viscosity damping nonlinear partial differential equations full weak solution |
| url | https://www.mdpi.com/2073-4360/14/18/3789 |
| work_keys_str_mv | AT evgeniisbaranovskii modelforaqueouspolymersolutionswithdampingtermsolvabilityandvanishingrelaxationlimit AT mikhailaartemov modelforaqueouspolymersolutionswithdampingtermsolvabilityandvanishingrelaxationlimit |