Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1805-1815.

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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;;
  • Supported by:
    the NSFC(11901346);the NSFC(11871305);the Research Fund for Excellent Dissertation of China Three Gorges University(2021SSPY148)


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

CLC Number: 

  • O175.2