Stochastic generalized magnetohydrodynamics equations: well-posedness

Abstract

In this paper, we study a stochastic magnetohydrodynamics system with fractional diffusion ${(-\mathrm{\Delta })}^{\alpha }$, $\alpha >0$, in ${\mathbb{R}}^d$, $d=2,3$. Our main goal is to identify the regularity of the driving noises and the conditions on $\alpha$ under which we can prove the existence of a martingale solution.

Keywords:

• Stochastic magnetohydrodynamics
• martingale solution
• Galerkin approximation

AMS Subject Classifications:

• 35H55
• 60H15
• 76D05
• 35Q30
• 76F20

Acknowledgements

Special thanks goes to Dr. Razafimandimby for discussions, comments and suggestions for improving this paper.

Notes

No potential conflict of interest was reported by the author.