This problem was addressed by George Keith Batchelor(1951), Keith Stewartson(1952) and many other researchers. Here the solution is not simple, because of the additional length scale imposed in the problem i.e., the distance  between the two disks. In addition, the uniqueness and existence of a steady solution are also depend on the corresponding Reynolds number .<br />
Then the boundary conditions for the fluid  are
In terms of , the upper wall location is simply . Thus, instead of the scalings 
used before, it is convenient to introduce following transformation,
so that the governing equations become
with six boundary conditions
and the pressure is given by
Here boundary conditions are six because pressure is not known either at the top or bottom wall;  is to be obtained as part of solution. For large Reynolds number , Batchelor argued that the fluid in the core would rotate at a constant velocity, flanked by two boundary layers at each disk for  and there would be two uniform counter-rotating flow of thickness  for . However, Stewartson predicted that for  the fluid in the core would not rotate at , but just left with two boundary layers at each disk. It turns out, Stewartson predictions were correct (see Stewartson layer).
There is also an exact solution if the two disks are rotating about different axes but for .