Abstract—The purpose of present paper is to establish the regularity of classical solution for second grade fluid. We consider unsteady flow passing through the porous medium. The incompressible fluid is taken between two rigid plates. We apply the magnetic field of the system and Darcy's law is performed due to porous medium. In addition uniqueness of classical solution is also verified. Finally neglecting the effect of porosity we obtain a unique classical solution of MHD second grade fluid.

Index Terms—Porous medium, second grade fluid, classical solution.

S. Rahman is with the Department of Applied Mathematics, Northwestern Polytechnical University, 710129, Xi'an, Shaanxi, P. R. China (e-mail: saeed@ciit.net.pk).
T. Hayat is with the Department of Mathematics, Quaid-i-Azam University 45320 Islamabad 44000, Pakistan.
Hamed H. Alsulami is with the Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.

Cite: S. Rahman, T. Hayat, and Hamed H. Alsulami, "Regularity for MHD Second Grade Fluid in a Porous Space," International Journal of Applied Physics and Mathematics vol. 4, no. 2, pp. 103-107, 2014.