分数阶扩散的MHD-Boussinesq系统的全局正则性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1805-1815.

分数阶扩散的MHD-Boussinesq系统的全局正则性

杨静¹(),邓雪梅^1,²(),周艳平^1,^2,*()

¹ 三峡大学理学院湖北宜昌 443002
² 三峡大学数学研究中心湖北宜昌 443002

收稿日期:2021-03-12 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 周艳平 E-mail:1972639378@qq.com;dxmeisx@126.com;zhyp5208@163.com
作者简介:杨静, E-mail:1972639378@qq.com|邓雪梅, E-mail:dxmeisx@126.com
基金资助:
国家自然科学基金(11901346);国家自然科学基金(11871305);三峡大学学位论文培优基金(2021SSPY148)

Global Regularity for the MHD-Boussinesq System with Fractional Diffusion

Jing Yang¹(),Xuemei Deng^1,²(),Yanping Zhou^1,^2,*()

¹ College of Science, China Three Gorges University, Hubei Yichang 443002
² Three Gorges Mathematical Research Center, China Three Gorges University, Hubei Yichang 443002

Received:2021-03-12 Online:2021-12-26 Published:2021-12-02
Contact: Yanping Zhou E-mail:1972639378@qq.com;dxmeisx@126.com;zhyp5208@163.com
Supported by:
the NSFC(11901346);the NSFC(11871305);the Research Fund for Excellent Dissertation of China Three Gorges University(2021SSPY148)

摘要/Abstract

摘要：

研究 $n（n\geq2）$ 维分数阶扩散的MHD-Boussinesq系统.当非负常数 $\alpha，\beta$ 及 $\gamma$ 满足 $\alpha\geq\frac{1}{2}+\frac{n}{4}$ ， $\alpha+\beta\geq 1+\frac{n}{2}$ 及 $\alpha+\gamma\geq\frac{n}{2}$ 时，利用能量方法，得到了MHD-Boussinesq系统全局解的存在唯一性，推广了已有的结果.

关键词: MHD-Boussinesq系统, 全局正则性, 分数阶扩散

Abstract:

In this paper, we investigate the $n$ -dimensional $(n\geq2)$ Magnetohydrodynamics-Boussinesq system with fractional diffusion. When the nonnegative constants $\alpha, \beta$ and $\gamma$ satisfy $\alpha\geq\frac{1}{2}+\frac{n}{4}, \ \alpha+\beta\geq 1+\frac{n}{2}$ and $\alpha+\gamma\geq\frac{n}{2}$ , by using the energy methods, we obtain the global existence and uniqueness of solution for the system, which generalizes the existing result.

Key words: MHD-Boussinesq system, Global regularity, Fractional diffusion

中图分类号:

O175.2

杨静,邓雪梅,周艳平. 分数阶扩散的MHD-Boussinesq系统的全局正则性[J]. 数学物理学报, 2021, 41(6): 1805-1815.

Jing Yang,Xuemei Deng,Yanping Zhou. Global Regularity for the MHD-Boussinesq System with Fractional Diffusion[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1805-1815.

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