Problem 2. (12 pts.) A viscous fluid is initially at rest in a circular container. At time zero, the outer boundary starts to rotate with a rotation rate, $2. Assuming the container is very long, the angular velocity depends only on time and radial position, ie., v=v(rit). The velocity v(r,() is governed by the following simplification of the Navier-Stokes equations: av/at = 0/or (1/ra(rv)/ar] V ( At ) IC: t=0, V=0 BC1: r= R, v= RQ BC2: r = 0, v ~ finite (a) Physical intuition suggests that as time t -> co, the fluid is in solid body rotation, i.e. v=r 2, 0