The continuous dependence for the Hall-MHD equations with fractional magnetic diffusion

ABSTRACT

In this paper, we show that the solutions to the incompressible Hall-MHD system with fractional magnetic diffusion depend continuously on the initial data in $H^s\left({\mathbb{R}}^d\right)$, $s>1+d/2$.

Keywords:

• Hall-MHD equations
• continuous dependence

AMS Subject Classifications:

• 76W05
• 35B30
• 35B35

Acknowledgments

The authors thank the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (NSFC) (No. 11361004).