A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations
In this paper, we proved the global (in time) regularity for smooth solution to the 2D generalized magneto-micropolar equations with zero viscosity. When there is no kinematic viscosity in the momentum equation, it is difficult to examine the bounds on the any derivatives of the velocity JεuL2. In o...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/1501851 |
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| author | Hui Zhang |
| author_facet | Hui Zhang |
| author_sort | Hui Zhang |
| collection | DOAJ |
| description | In this paper, we proved the global (in time) regularity for smooth solution to the 2D generalized magneto-micropolar equations with zero viscosity. When there is no kinematic viscosity in the momentum equation, it is difficult to examine the bounds on the any derivatives of the velocity JεuL2. In order to overcome the main obstacle, we find a new unknown quantity which is by combining the vorticity and the microrotation angular velocity; the structure of the system including the combined quantity obeys a Beale–Kato–Majda criterion. Moreover, the maximal regularity of parabolic equations together with the classic commutator estimates allows us to derive the Hs estimates for solutions of the system. |
| format | Article |
| id | doaj-art-2dd5fdf0ab6046d4a2ae7a2309144172 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-2dd5fdf0ab6046d4a2ae7a23091441722025-08-20T03:55:06ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/1501851A Global Regularity Result for the 2D Generalized Magneto-Micropolar EquationsHui Zhang0College of Mathematical and Physical ScienceIn this paper, we proved the global (in time) regularity for smooth solution to the 2D generalized magneto-micropolar equations with zero viscosity. When there is no kinematic viscosity in the momentum equation, it is difficult to examine the bounds on the any derivatives of the velocity JεuL2. In order to overcome the main obstacle, we find a new unknown quantity which is by combining the vorticity and the microrotation angular velocity; the structure of the system including the combined quantity obeys a Beale–Kato–Majda criterion. Moreover, the maximal regularity of parabolic equations together with the classic commutator estimates allows us to derive the Hs estimates for solutions of the system.http://dx.doi.org/10.1155/2022/1501851 |
| spellingShingle | Hui Zhang A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations Journal of Function Spaces |
| title | A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations |
| title_full | A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations |
| title_fullStr | A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations |
| title_full_unstemmed | A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations |
| title_short | A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations |
| title_sort | global regularity result for the 2d generalized magneto micropolar equations |
| url | http://dx.doi.org/10.1155/2022/1501851 |
| work_keys_str_mv | AT huizhang aglobalregularityresultforthe2dgeneralizedmagnetomicropolarequations AT huizhang globalregularityresultforthe2dgeneralizedmagnetomicropolarequations |