Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids
The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2020-08-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.04.001/full/pdf |
| _version_ | 1797791612696264704 |
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| author | Dongming Wei Samer Al-Ashhab |
| author_facet | Dongming Wei Samer Al-Ashhab |
| author_sort | Dongming Wei |
| collection | DOAJ |
| description | The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results. |
| first_indexed | 2024-03-13T02:21:17Z |
| format | Article |
| id | doaj.art-b4ffd433a4a948b394cc9aac6ea082ec |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:21:17Z |
| publishDate | 2020-08-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-b4ffd433a4a948b394cc9aac6ea082ec2023-06-30T09:27:54ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142020-08-01261/216717810.1016/j.ajmsc.2019.04.001Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluidsDongming Wei0Samer Al-Ashhab1Department of Mathematics, Nazarbayev University, Astana, KazakhstanDepartment of Mathematics and Statistics, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi ArabiaThe reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.04.001/full/pdfNon-linear boundary value problemSingularSelf-similar transformationExistenceUniqueness |
| spellingShingle | Dongming Wei Samer Al-Ashhab Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids Arab Journal of Mathematical Sciences Non-linear boundary value problem Singular Self-similar transformation Existence Uniqueness |
| title | Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids |
| title_full | Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids |
| title_fullStr | Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids |
| title_full_unstemmed | Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids |
| title_short | Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids |
| title_sort | existence of self similar solutions of the two dimensional navier stokes equation for non newtonian fluids |
| topic | Non-linear boundary value problem Singular Self-similar transformation Existence Uniqueness |
| url | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.04.001/full/pdf |
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