Global solutions for the time-space fractional rotating magnetohydrodynamic equations in Besov spaces

Abstract

This paper is devoted to the time-space fractional rotating magnetohydrodynamic equations in Besov spaces. By exploiting the interweaving action of the smoothing effects of the fractional Laplacian dissipation and dispersive effects of the Coriolis force involving with the time-fractional evolution mechanism, the existence and uniqueness of global mild solutions are obtained under some smallness conditions by employing Mittag-Leffler operators families and contraction mapping principle. It is worth mentioning that our result permits the initial velocity to be arbitrarily large provided that the rotation parameter is sufficiently large.