There are two parallel plates, upper plate is static and bottom plate is porous and in motion. At the same time there are types of motion in bottom plate. Plate is oscillating with velocity Uo*e^(iwt) and also moving forward along X-Axis with constant velocity Co. Due to motion in plate Newtonian and Imcompressible fluid is injected with velocity Wo<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">Velocity field is given<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">V=[u(y,t),Wo,0]<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">BC's: u(0,t)=Uo*e^(iwt)<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">u(d,t)=0<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">IC's: u(y,0)=0<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">In the start we used the "Galilean transform" <br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">Let y=Y-c0t

From what I could gather around the incredibly poorly posted text, you want the Navier Stokes equations.