Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions
In this article, we investigate the Euler-α\alpha equations in a three-dimensional bounded domain. On the one hand, we prove in the Euler setting that the equations are locally well-posed with initial data in Hs(s≥3){H}^{s}\left(s\ge 3). On the other hand, the relationship between the Hs{H}^{s}-nor...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0077 |
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| _version_ | 1846171070703337472 |
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| author | Yuan Shaoliang Huang Lehui Cheng Lin You Xiaoguang |
| author_facet | Yuan Shaoliang Huang Lehui Cheng Lin You Xiaoguang |
| author_sort | Yuan Shaoliang |
| collection | DOAJ |
| description | In this article, we investigate the Euler-α\alpha equations in a three-dimensional bounded domain. On the one hand, we prove in the Euler setting that the equations are locally well-posed with initial data in Hs(s≥3){H}^{s}\left(s\ge 3). On the other hand, the relationship between the Hs{H}^{s}-norm of the velocity field and the parameter α\alpha is clarified. |
| format | Article |
| id | doaj-art-c9c2b5b1d37e4eaaa8f23a167671725d |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-c9c2b5b1d37e4eaaa8f23a167671725d2024-11-11T08:36:39ZengDe GruyterOpen Mathematics2391-54552024-11-012214173417710.1515/math-2024-0077Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditionsYuan Shaoliang0Huang Lehui1Cheng Lin2You Xiaoguang3School of Big Data and Artificial Intelligence, Fujian Polytechnic Normal University, Fuzhou, Fujian, 350300, P. R. ChinaCenter For Educational Technology and Information, Jiangxi Science and Technology Normal University, Nanchang, Jiangxi, 330038, P. R. ChinaCollege of Artificial Intelligence, Jiangxi Science and Technology Normal University, Nanchang, Jiangxi, 330038, P. R. ChinaSchool of Mathematics, Jiangxi Science and Technology Normal University, Nanchang, Jiangxi, 330038, P. R. ChinaIn this article, we investigate the Euler-α\alpha equations in a three-dimensional bounded domain. On the one hand, we prove in the Euler setting that the equations are locally well-posed with initial data in Hs(s≥3){H}^{s}\left(s\ge 3). On the other hand, the relationship between the Hs{H}^{s}-norm of the velocity field and the parameter α\alpha is clarified.https://doi.org/10.1515/math-2024-0077non-newtonian fluidswell-posedness for pdeseuler-α equationseuler equations35a0135d3535q35 |
| spellingShingle | Yuan Shaoliang Huang Lehui Cheng Lin You Xiaoguang Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions Open Mathematics non-newtonian fluids well-posedness for pdes euler-α equations euler equations 35a01 35d35 35q35 |
| title | Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions |
| title_full | Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions |
| title_fullStr | Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions |
| title_full_unstemmed | Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions |
| title_short | Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions |
| title_sort | euler α equations in a three dimensional bounded domain with dirichlet boundary conditions |
| topic | non-newtonian fluids well-posedness for pdes euler-α equations euler equations 35a01 35d35 35q35 |
| url | https://doi.org/10.1515/math-2024-0077 |
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