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

• 论文 • 上一篇    下一篇

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. 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 Deng1,2(),Yanping Zhou1,2,*()   

  1. 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:

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