# American Institute of Mathematical Sciences

## Global well-posedness of a 3D Stokes-Magneto equations with fractional magnetic diffusion

 School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510520, China

* Corresponding author: Wen Tan

Received  April 2020 Published  July 2020

Fund Project: The first author is supported by NSFC grant 11701099, The second author is supported by NSFC grant 11871346

This paper is devoted to the global well-posedness of a three-dimensional Stokes-Magneto equations with fractional magnetic diffusion. It is proved that the equations admit a unique global-in-time strong solution for arbitrary initial data when the fractional index $\alpha\ge\frac32$. This result might have a potential application in the theory of magnetic relaxtion.

Citation: Yingdan Ji, Wen Tan. Global well-posedness of a 3D Stokes-Magneto equations with fractional magnetic diffusion. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020227
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