Convergence rates for a rotating MHD system with evanescent viscosity

Abstract

In this article, we focus on a MHD model that takes into account the Coriolis force. In this case, the strength of the rotation is measured by the Rossby number $\hat{I}\mu$ (positive). Under the assumption that the rotation is strong (that is, when $\hat{I}\mu$ goes to zero) and the kinematic viscosity goes to zero as $\hat{I}\mu$^$\hat{I}\pm$ ($\hat{I}\pm$ positive), we first establish the global convergence of weak solutions, and then prove the global existence and convergence of strong solutions. In particular, the Strichartz estimates used to obtain explicit convergence rates depend on the above parameter $\hat{I}\pm$ and lead us to identify an admissible interval for $\hat{I}\pm$.