Global regularity for unsteady flow of MHD Sisko fluid in a porous medium

The aim of the present paper is to establish the global regularity of classical solution for unidirectional flow of magnetohydrodynamic (MHD) Sisko fluid. The fluid is taken between two rigid plates. An incompressible fluid saturates the porous medium. The main interest in this paper is to establish the global regularity of classical solutions when [Formula: see text], [Formula: see text], and [Formula: see text] are sufficiently small. In addition, uniqueness of the classical solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, V is the velocity, u is the x-component of velocity, and [Formula: see text] is the vorticity.