Fundamental Serrin Type Regularity Criteria for 3D MHD Fluid Passing Through the Porous Medium

Abstract

In this paper, we consider the Cauchy problem for the $3$D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for $3$D MHD fluid passing through the porous medium in terms of gradient pressure, {\it J. Comput. Appl. Math.}, {\bf 270} (2014), 88--99].