Abstract
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 parallel to u parallel to(2)(BMO), parallel to w parallel to(2)(BMO), and parallel to partial derivative w/partial derivative y parallel to(2)(BMO) 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 w = del x (V) over bar = (partial derivative u/partial derivative y) is the vorticity.