The Magnetohydrodynamic (MHD) plasma Couette flow in a rotating frame of reference subject to the Hall current is studied. This problem is confined to a startup process, which deals with an impulsive start of the moving plate as well as an accelerated start of the moving plate. The solution is obtained by employing the Laplace inversion method. An asymptotic behavior of the solution is analysed for small as well as large time T to gain the physical insight into the flow pattern. As a consequence of the physical situation of interest the fully ionized neutral plasma interacts with the frictional layer when it starts in motion. The dimensionless velocity profiles are depicted graphically and the shear stresses are presented in tables.
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