New regularity criteria for an mhd darcy-forchheimer fluid

The purpose of the presented article is to develop some new global regularity criteria for a magnetohydrodynamic (MHD) fluid flowing in a saturated porous medium. The effect of the porous medium, over the fluid flow, is characterized by a Darcy-Forchheimer law. The fluid, under study, is considered as one-dimensional and flowing in the x-direction with velocity component u. In addition, such a component is assumed to vary with the y-direction, i.e. u(y). Then, given the vorticity function w=-(partial derivative u)(partial derivative y), such that & Vert;W & Vert;(2)(BMO) is sufficiently small, we develop the regularity criteria under the scope of the L-2 space. We extend our results to the spaces L-s, where s > 2. Afterward, we prove the Liouville-type theorem for the MHD Darcy-Forchheimer flow equation. Eventually, we obtain some characterization about the asymptotic behaviour of solutions, particularly, the nonuniform convergence in L-2 for t ->infinity