A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model
In this note, we prove the existence and uniqueness of weak solutions for the boundary value problem modelling the stationary case of the bioconvective flow problem. The bioconvective model is a boundary value problem for a system of four equations: the nonlinear Stokes equation, the incompressibili...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/4051812 |
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| _version_ | 1832555510883155968 |
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| author | Aníbal Coronel Luis Friz Ian Hess Alex Tello |
| author_facet | Aníbal Coronel Luis Friz Ian Hess Alex Tello |
| author_sort | Aníbal Coronel |
| collection | DOAJ |
| description | In this note, we prove the existence and uniqueness of weak solutions for the boundary value problem modelling the stationary case of the bioconvective flow problem. The bioconvective model is a boundary value problem for a system of four equations: the nonlinear Stokes equation, the incompressibility equation, and two transport equations. The unknowns of the model are the velocity of the fluid, the pressure of the fluid, the local concentration of microorganisms, and the oxygen concentration. We derive some appropriate a priori estimates for the weak solution, which implies the existence, by application of Gossez theorem, and the uniqueness by standard methodology of comparison of two arbitrary solutions. |
| format | Article |
| id | doaj-art-082270fcec744745ad556484e5617f0f |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-082270fcec744745ad556484e5617f0f2025-02-03T05:47:58ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/40518124051812A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow ModelAníbal Coronel0Luis Friz1Ian Hess2Alex Tello3GMA, Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán, ChileGMA, Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán, ChileGMA, Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán, ChileGMA, Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán, ChileIn this note, we prove the existence and uniqueness of weak solutions for the boundary value problem modelling the stationary case of the bioconvective flow problem. The bioconvective model is a boundary value problem for a system of four equations: the nonlinear Stokes equation, the incompressibility equation, and two transport equations. The unknowns of the model are the velocity of the fluid, the pressure of the fluid, the local concentration of microorganisms, and the oxygen concentration. We derive some appropriate a priori estimates for the weak solution, which implies the existence, by application of Gossez theorem, and the uniqueness by standard methodology of comparison of two arbitrary solutions.http://dx.doi.org/10.1155/2018/4051812 |
| spellingShingle | Aníbal Coronel Luis Friz Ian Hess Alex Tello A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model Journal of Function Spaces |
| title | A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model |
| title_full | A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model |
| title_fullStr | A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model |
| title_full_unstemmed | A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model |
| title_short | A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model |
| title_sort | result on the existence and uniqueness of stationary solutions for a bioconvective flow model |
| url | http://dx.doi.org/10.1155/2018/4051812 |
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