Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition
In this paper, we consider the evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under the Rauch condition, we use the Galerkin approximation method and...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6573219 |
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| author | Hicham Mahdioui Sultana Ben Aadi Khalid Akhlil |
| author_facet | Hicham Mahdioui Sultana Ben Aadi Khalid Akhlil |
| author_sort | Hicham Mahdioui |
| collection | DOAJ |
| description | In this paper, we consider the evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under the Rauch condition, we use the Galerkin approximation method and a weak precompactness criterion to ensure the convergence to a desired solution. Moreover, a control problem associated with such system of equations is studied with the help of a stability result with respect to the external forces. At the end of this paper, a more general condition due to Z. Naniewicz, namely the directional growth condition, is considered and all the results are reexamined. |
| format | Article |
| id | doaj-art-98dc666a942a4db9b2c6d161b9c42eeb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-98dc666a942a4db9b2c6d161b9c42eeb2025-02-03T01:20:21ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/65732196573219Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch ConditionHicham Mahdioui0Sultana Ben Aadi1Khalid Akhlil2Ibn Zohr University, MoroccoIbn Zohr University, MoroccoIbn Zohr University, MoroccoIn this paper, we consider the evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under the Rauch condition, we use the Galerkin approximation method and a weak precompactness criterion to ensure the convergence to a desired solution. Moreover, a control problem associated with such system of equations is studied with the help of a stability result with respect to the external forces. At the end of this paper, a more general condition due to Z. Naniewicz, namely the directional growth condition, is considered and all the results are reexamined.http://dx.doi.org/10.1155/2020/6573219 |
| spellingShingle | Hicham Mahdioui Sultana Ben Aadi Khalid Akhlil Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition Journal of Function Spaces |
| title | Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition |
| title_full | Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition |
| title_fullStr | Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition |
| title_full_unstemmed | Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition |
| title_short | Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition |
| title_sort | weak solutions and optimal control of hemivariational evolutionary navier stokes equations under rauch condition |
| url | http://dx.doi.org/10.1155/2020/6573219 |
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