The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type
In this paper, we are concerned with the nonsteady Boussinesq system under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions, velocity, static (or total) pressure, rotation, and stress (or total stress) together, and the boundary...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/6096531 |
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| author | Tujin Kim |
| author_facet | Tujin Kim |
| author_sort | Tujin Kim |
| collection | DOAJ |
| description | In this paper, we are concerned with the nonsteady Boussinesq system under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions, velocity, static (or total) pressure, rotation, and stress (or total stress) together, and the boundary conditions for temperature may include Dirichlet, Neumann, and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity, and shape of the boundary surface, we get variational formulation. The formulations consist of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. For the case of boundary conditions including the static pressure and stress, we prove that if the data of the problem are small enough and compatibility conditions at the initial instance are satisfied, then there exists a unique solution on the given interval. For the case of boundary conditions including the total pressure and total stress, we prove the existence of a solution without restriction on the data and parameters of the problem. |
| format | Article |
| id | doaj-art-decb01ee31a042da8114419d2b3adf11 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-decb01ee31a042da8114419d2b3adf112025-02-03T01:28:17ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/60965316096531The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction TypeTujin Kim0Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People’s Republic of KoreaIn this paper, we are concerned with the nonsteady Boussinesq system under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions, velocity, static (or total) pressure, rotation, and stress (or total stress) together, and the boundary conditions for temperature may include Dirichlet, Neumann, and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity, and shape of the boundary surface, we get variational formulation. The formulations consist of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. For the case of boundary conditions including the static pressure and stress, we prove that if the data of the problem are small enough and compatibility conditions at the initial instance are satisfied, then there exists a unique solution on the given interval. For the case of boundary conditions including the total pressure and total stress, we prove the existence of a solution without restriction on the data and parameters of the problem.http://dx.doi.org/10.1155/2020/6096531 |
| spellingShingle | Tujin Kim The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type International Journal of Differential Equations |
| title | The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type |
| title_full | The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type |
| title_fullStr | The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type |
| title_full_unstemmed | The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type |
| title_short | The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type |
| title_sort | nonsteady boussinesq system with mixed boundary conditions including conditions of friction type |
| url | http://dx.doi.org/10.1155/2020/6096531 |
| work_keys_str_mv | AT tujinkim thenonsteadyboussinesqsystemwithmixedboundaryconditionsincludingconditionsoffrictiontype AT tujinkim nonsteadyboussinesqsystemwithmixedboundaryconditionsincludingconditionsoffrictiontype |