Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性)
The purpose of this paper is to study the global well-posedness of generalized MHD-Boussinesq equations with only velocity dissipation in whole space Rn (n≥2). Firstly, by exploiting the structure of this system, we obtain the uniform L2-bound of the global solutions. Then, the uniform H1-bound of t...
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Zhejiang University Press
2024-09-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
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| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2024.05.006 |
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| author | 杜美华(DU Meihua) |
| author_facet | 杜美华(DU Meihua) |
| author_sort | 杜美华(DU Meihua) |
| collection | DOAJ |
| description | The purpose of this paper is to study the global well-posedness of generalized MHD-Boussinesq equations with only velocity dissipation in whole space Rn (n≥2). Firstly, by exploiting the structure of this system, we obtain the uniform L2-bound of the global solutions. Then, the uniform H1-bound of the global solutions is proved by making use of logarithmic type interpolation inequality and the improved Gronwall inequality. Finally, by using delicate energy estimates, we overcome the difficulty of lack of dissipation and establish the a priori uniform Hss>1+n/2 estimate which proves the global existence and uniqueness of the classical solutions to this system.(在全空间Rn（n≥2）中研究仅具有速度场耗散的广义磁Boussinesq方程的整体适定性。首先，利用方程的结构得到整体解的一致L2界；然后，利用对数型的插值不等式和改进的Gronwall 不等式证明了整体解的一致H1界；最后，利用精细的能量估计，克服方程耗散缺失带来的困难，建立了解的整体一致Hss>1+n/2先验估计，证明了该方程经典解的整体存在唯一性。) |
| format | Article |
| id | doaj-art-bdea1ff2b5ab4ae490d2bf2949649e8d |
| institution | DOAJ |
| issn | 1008-9497 |
| language | zho |
| publishDate | 2024-09-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj-art-bdea1ff2b5ab4ae490d2bf2949649e8d2025-08-20T02:48:46ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972024-09-0151556857110.3785/j.issn.1008-9497.2024.05.006Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性)杜美华(DU Meihua)0https://orcid.org/0009-0004-5606-7834Department of Basic， Qingdao West Coast New District Senior Vocational and Technical School， Qingdao 266000， Shandong Province， China(青岛西海岸新区高级职业技术学校 基础部，山东 青岛 266000)The purpose of this paper is to study the global well-posedness of generalized MHD-Boussinesq equations with only velocity dissipation in whole space Rn (n≥2). Firstly, by exploiting the structure of this system, we obtain the uniform L2-bound of the global solutions. Then, the uniform H1-bound of the global solutions is proved by making use of logarithmic type interpolation inequality and the improved Gronwall inequality. Finally, by using delicate energy estimates, we overcome the difficulty of lack of dissipation and establish the a priori uniform Hss>1+n/2 estimate which proves the global existence and uniqueness of the classical solutions to this system.(在全空间Rn（n≥2）中研究仅具有速度场耗散的广义磁Boussinesq方程的整体适定性。首先，利用方程的结构得到整体解的一致L2界；然后，利用对数型的插值不等式和改进的Gronwall 不等式证明了整体解的一致H1界；最后，利用精细的能量估计，克服方程耗散缺失带来的困难，建立了解的整体一致Hss>1+n/2先验估计，证明了该方程经典解的整体存在唯一性。)https://doi.org/10.3785/j.issn.1008-9497.2024.05.006generalized mhd-boussinesq equations(广义磁boussinesq方程)partial dissipation(部分耗散)global regularity(整体正则性) |
| spellingShingle | 杜美华(DU Meihua) Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性) Zhejiang Daxue xuebao. Lixue ban generalized mhd-boussinesq equations(广义磁boussinesq方程) partial dissipation(部分耗散) global regularity(整体正则性) |
| title | Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性) |
| title_full | Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性) |
| title_fullStr | Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性) |
| title_full_unstemmed | Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性) |
| title_short | Global regularity of generalized MHD-Boussinesq equations(广义磁Boussinesq方程的整体正则性) |
| title_sort | global regularity of generalized mhd boussinesq equations 广义磁boussinesq方程的整体正则性 |
| topic | generalized mhd-boussinesq equations(广义磁boussinesq方程) partial dissipation(部分耗散) global regularity(整体正则性) |
| url | https://doi.org/10.3785/j.issn.1008-9497.2024.05.006 |
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